Krsna created Srimati Radharani just so He could experience loving effection, exchanges and association with a women.

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī." (Srimad Bhagavatam Canto 3 Chapter 31 text 38, Purport)

Krsna created Srimati Radharani just so He could experience loving effection, exchanges and association with a women, because real love can only be realized and exist when there are "two" in the relationship.

Srimati Rādhārāṇī is the manifestation of the pleasure potency of Krsna the Supreme Personality of Godhead and is His direct expansion. 

Srila Prabhupada - "Love means two, there must be two, the lover and the beloved." (Lecture on BG Chapter 9 text 2-5, New York, Nov 23, 1966)

Srila Prabhupāda - “If one asks about the origin of love of Kṛṣṇa, the answer is that the origin is in Śrīmatī Rādhārāṇī alone. So who is the most dear friend of Kṛṣṇa? The answer again is Śrīmatī Rādhārāṇī alone. No one else." (CC Madhya 8.182, Translation and Purport)

Srila Prabhupada - "Since all transcendental qualities are manifested in Śrīmatī Rādhārāṇī, She alone is able to fulfill all the desires of Kṛṣṇa. No one else." (CC Madhya 8.182, Translation and Purport)

Srila Prabhupada - "When Kṛṣṇa left Vṛndāvana for Mathurā, the gopīs became most dejected and spent the rest of their lives simply crying in separation from Kṛṣṇa. 

This means that in one sense they were never actually separated from Kṛṣṇa. There is no difference between thinking of Kṛṣṇa and associating with Him. Thinking of Kṛṣṇa in separation, as Śrī Caitanya Mahāprabhu did, is far better than serving Kṛṣṇa directly." (Nectar of Instruction 10, Purport)

Srila Prabhupada - "Of all the devotees who have developed unalloyed devotional love for Kṛṣṇa, the gopīs are most exalted, and out of all these exalted gopīs, Śrīmatī Rādhārāṇī is the highest. 

No one can excel the devotional service of Śrīmatī Rādhārāṇī. 

Indeed, even Kṛṣṇa cannot understand the attitude of Śrīmatī Rādhārāṇī; therefore He took Her position and appeared as Śrī Caitanya Mahāprabhu, just to understand Her transcendental feelings." (Nectar of Instruction 10, Purport) 

Srila Prabhupada - "In this way Śrīla Rūpa Gosvāmī concludes that Śrīmatī Rādhārāṇī is the most exalted devotee of Kṛṣṇa and that Her kuṇḍa (lake), Śrī Rādhā-kuṇḍa, is the most exalted place."(Nectar of Instruction 10, Purport)

Srila Prabhupada - "As Kṛṣṇa is the highest emblem of spiritual perfection, so Rādhārāṇī is the highest emblem of that spiritual pleasure potency by which Kṛṣṇa is satisfied. Since Kṛṣṇa is unlimited, in order to satisfy Him Rādhārāṇī is also unlimited. 

Kṛṣṇa is satisfied just by seeing Rādhārāṇī, but Rādhārāṇī expands Herself in such a way that Kṛṣṇa desires to enjoy Her more. 

Because Kṛṣṇa was unable to estimate the pleasure potency of Rādhārāṇī, He decided to accept the role of Rādhārāṇī, and that combination is Śrī Caitanya Mahāprabhu." (Teachings of Lord Caitanya, Chapter 31)

Srila Prabhupada - "Among the gopīs, Śrīmatī Rādhikā (Srimati Radharani) is the foremost. She surpasses all in beauty, in good qualities, in good fortune and, above all, in love." (Caitanya Caritamrta Adi 4.214, Translation and Purport)

Srila Prabhupāda - "Among all the gopīs, Śrīmatī Rādhārāṇī is the most exalted. She is the most beautiful, the most qualified and, above all, the greatest lover of Kṛṣṇa." (Caitanya Caritamrta Adi 4.214, Translation and Purport)

Srila Prabhupada - "Rādhā is the beloved consort of Kṛṣṇa, and She is the wealth of His life. Without Her, the gopīs cannot give Him pleasure. Radharani is the chief damsel of Vraja in love with Govinda, the Supreme Personality of Godhead, Śrī Kṛṣṇa." (Caitanya Caritamrta Adi 4.218, Translation)

Srila Prabhupada - "The fact is that both Kṛṣṇa and Lord Caitanya are the original Personality of Godhead. No one should try to eliminate Lord Caitanya from Śrī Kṛṣṇa. In His form of Śrī Kṛṣṇa, He is the supreme enjoyer, and in His form of Lord Caitanya, He is the supreme enjoyed." (TLC, from Chapter 32)

Srila Prabhupada - "No one can be more superexcellently attractive than Śrī Kṛṣṇa, and but for Śrī Kṛṣṇa, no one can enjoy the supreme form of devotion, Śrīmatī Rādhārāṇī. But for Śrī Kṛṣṇa, all Viṣṇu forms are lacking this ability. This is explained in the description of Govinda in Caitanya-caritāmṛta. 

There it is said that Śrīmatī Rādhārāṇī is the only personality who can infuse Śrī Kṛṣṇa with transcendental pleasure. Thus Śrīmatī Rādhārāṇī is the chief damsel of Vraja in love with Govinda, the Supreme Personality of Godhead, Śrī Kṛṣṇa." (TLC, from Chapter 32)

Srila Prabhupada - ''We have got the propensity to love. Love means somebody else. Love cannot be one or love cannot be executed by only one, there must be another one. I love somebody; somebody loves me, there must be lover, there must be beloved, and the transaction, then there is love." (Lecture on Srimad Bhagavatam Canto 1 Chapter 2 text 6, Delhi, November 12, 1973)

Srila Prabhupāda – ''Unless there are two persons, where is the question of love? Love means two persons, then there is exchange, then there is love. I must deal with you open-hearted, you must deal with me open-hearted, then there is love. So if you want to love Kṛṣṇa, God, then these things must be there." (August 9, 1976, Tehran)

Srila Prabhupada - "Rādhā and Kṛṣṇa are one and the same, but They have assumed two bodies. Thus They enjoy each other, tasting the mellows of love. The two transcendentalists Rādhā and Kṛṣṇa are a puzzle to materialists. The description of Rādhā and Kṛṣṇa from the diary of Śrīla Svarūpa Dāmodara Gosvāmī is a condensed explanation, but one needs great spiritual insight to understand the mystery of these two personalities. One is enjoying in two." (Caitanya Caritamrita Adi 4.56, Translation and Purport)

Srila Prabhupada - "Śrī Kṛṣṇa is the potent factor, and Śrīmatī Rādhārāṇī is the internal potency. According to Vedānta philosophy, there is no difference between the potent and the potency; they are identical. We cannot differentiate between one and the other, any more than we can separate fire from heat." (Caitanya Caritamrita Adi 4.56, Translation and Purport)

Srila Prabhupada - "Everything in the Absolute is inconceivable in relative existence. Therefore in relative cognizance it is very difficult to assimilate this truth of the oneness between the potent and the potency. The philosophy of inconceivable oneness and difference propounded by Lord Caitanya is the only source of understanding for such intricacies of transcendence. In fact, Rādhārāṇī is the internal potency of Śrī Kṛṣṇa, and She eternally intensifies the pleasure of Śrī Kṛṣṇa." (Caitanya Caritamrita Adi 4.56, Translation and Purport) 

Srila Prabhupada - "The Impersonalists cannot understand this without the help of a mahā-bhāgavata devotee. The very name “Rādhā” suggests that Śrīmatī Rādhārāṇī is eternally the topmost mistress of the comforts of Śrī Kṛṣṇa. As such, She is the medium transmitting the living entities service to Śrī Kṛṣṇa. Devotees in Vṛndāvana therefore seek the mercy of Śrīmatī Rādhārāṇī in order to be recognized as loving servitors of Śrī Kṛṣṇa." (Caitanya Caritamrita Adi 4.56, Translation and Purport)

Srila Prabhupada - "As Kṛṣṇa is the highest emblem of spiritual perfection, so Rādhārāṇī is the highest emblem of that spiritual pleasure potency by which Kṛṣṇa is satisfied. Since Kṛṣṇa is unlimited, in order to satisfy Him Rādhārāṇī is also unlimited. 

Kṛṣṇa is satisfied just by seeing Rādhārāṇī, but Rādhārāṇī expands Herself in such a way that Kṛṣṇa desires to enjoy Her more. Because Kṛṣṇa was unable to estimate the pleasure potency of Rādhārāṇī, He decided to accept the role of Rādhārāṇī, and that combination is Śrī Caitanya Mahāprabhu." (Teachings of Lord Caitanya, Chapter 31)

Srila Prabhupada - "Of all the devotees who have developed unalloyed devotional love for Kṛṣṇa, the gopīs are most exalted, and out of all these exalted gopīs, Śrīmatī Rādhārāṇī is the highest. No one can excel the devotional service of Śrīmatī Rādhārāṇī. 

Indeed, even Kṛṣṇa cannot understand the attitude of Śrīmatī Rādhārāṇī; therefore He took Her position and appeared as Śrī Caitanya Mahāprabhu, just to understand Her transcendental feelings. (Nectar of Instruction 10, Purport)

Srila Prabhupada - "So our business is that we have to take shelter. Instead of taking shelter of the external energy. That is also Kṛṣṇa." (Lecture on BG 4.11 -- Vrndavana, August 3, 1974)

Srila Prabhupada - "There is no doubt, Kṛṣṇa, everything Kṛṣṇa's energy - nondifferent, but that is not very beneficial to us. We have to take shelter of the internal energy and Śrīmatī Rādhārāṇī is the symbol of internal energy. 

Therefore we take shelter of Śrīmatī Rādhārāṇī in Vṛndāvana, and that is our perfection of life. Then it will be easier to associate with Kṛṣṇa very easily. That should be our motto." (Lecture on BG 4.11, Vrndavana, August 3, 1974)

Srila Prabhupada – "Love is reciprocal, voluntary, good exchange of feeling. Then there is love. Not by force, no, Krsna does not want to become a lover like that." (July 8, 1976)

For Krsna to experience the love Srimati Radharani has for Him, Krsna and Radha become "one Body." And that one Body is Lord Caitanya Mahaprabhu.

Srila Prabhupada - "In his epic Caitanya-caritāmṛta, Kṛṣṇadāsa Kavirāja Gosvāmī has stressed that Lord Caitanya appeared for three principal purposes of His own. 

The first purpose was to relish the position of Śrīmatī Rādhārāṇī, who is the prime reciprocator of transcendental love of Śrī Kṛṣṇa. Lord Kṛṣṇa is the reservoir of transcendental loving transactions with Śrīmatī Rādhārāṇī. 

The subject of those loving transactions is the Lord Himself, and Rādhārāṇī is the object. Thus the subject, the Lord, wanted to relish the loving mellow in the position of the object, Rādhārāṇī.

The second reason for His appearance was to understand the transcendental mellow of Himself. Lord Kṛṣṇa is all sweetness. 

Rādhārāṇī’s attraction for Kṛṣṇa is sublime, and to experience that attraction and understand the transcendental sweetness of Himself, He accepted the mentality of Rādhārāṇī.

The third reason that Lord Caitanya appeared was to enjoy the bliss tasted by Rādhārāṇī. The Lord thought that undoubtedly Rādhārāṇī enjoyed His company and He enjoyed the company of Rādhārāṇī, but the exchange of transcendental mellow between the spiritual couple was more pleasing to Śrīmatī Rādhārāṇī than to Śrī Kṛṣṇa. 

Rādhārāṇī felt more transcendental pleasure in the company of Kṛṣṇa than He could understand without taking Her position, but for Śrī Kṛṣṇa to enjoy in the position of Śrīmatī Rādhārāṇī was impossible because that position was completely foreign to Him. 

Kṛṣṇa is the transcendental male, and Rādhārāṇī is the transcendental female. Therefore, to know the transcendental pleasure of loving Kṛṣṇa, Lord Kṛṣṇa Himself appeared as Lord Caitanya, accepting the emotions and bodily luster of Śrīmatī Rādhārāṇī.

Lord Caitanya appeared in order to fulfill these confidential desires, and also to preach the special significance of chanting 

Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare

And to answer the call of Advaita Prabhu. These were secondary reasons." (Caitanya Caritamrita Adi 4, Purport)

Srila Prabhupada - "Svarūpa Dāmodara Gosvāmī has described Lord Caitanya as Kṛṣṇa Himself with the attitude of Rādhārāṇī, or a combination of Rādhā and Kṛṣṇa. The intention of Lord Caitanya is to taste Kṛṣṇa’s sweetness in transcendental love. He does not care to think of Himself as Kṛṣṇa, because He wants the position of Rādhārāṇī. We should remember this. 

A class of so-called devotees called the nadīyā-nāgarīs or gaura-nāgarīs pretend that they have the sentiment of gopīs toward Lord Caitanya, but they do not realize that He placed Himself not as the enjoyer, Kṛṣṇa, but as the enjoyed, the devotee of Kṛṣṇa. The original reason that Lord Śrī Kṛṣṇa descended as Śrī Caitanya Mahāprabhu was to understand Śrīmatī Rādhārāṇī’s love for Kṛṣṇa and to taste that love." (CC Adi 4.41, Purport)

Srila Prabhupada  - "The original reason that Lord Śrī Kṛṣṇa descended as Śrī Caitanya Mahāprabhu was to understand Śrīmatī Rādhārāṇī’s love for Kṛṣṇa and to taste that love. The fruits of the tree of devotional service were innumerable, and therefore He wanted to distribute them unrestrictedly to everyone. 

Śrīla Rūpa Gosvāmī therefore writes-

anarpita-carīṁ cirāt karuṇayāvatīrṇaḥ kalausamarpayitum unnatojjvala-rasāṁ sva-bhakti-śriyamhariḥ puraṭa-sundara-dyuti-kadamba-sandīpitaḥ sadā hṛdaya-kandare sphuratu vaḥ śacī-nandanaḥ

There were many previous incarnations of the Supreme Personality of Godhead, but none were so generous, kind and magnanimous as Śrī Caitanya Mahāprabhu, for He distributed the most confidential aspect of devotional service, namely, the conjugal love of Rādhā and Kṛṣṇa. 

Therefore Śrī Rūpa Gosvāmī Prabhupāda desires that Śrī Caitanya Mahāprabhu live perpetually in the hearts of all devotees, for thus they can understand and relish the loving affairs of Śrīmatī Rādhārāṇī and Kṛṣṇa. Lord Caitanya is Kṛṣṇa with the feelings of Rādhārāṇī; in other words, He is a combination of Rādhā and Kṛṣṇa." (CC Adi 9.37, Purport)

Srila Prabhupada - "In separation from Kṛṣṇa, Śrī Caitanya Mahāprabhu relished all these ecstatic activities, and thus He fulfilled His own desires. 

In the beginning of the Caitanya-caritāmṛta it is said that Lord Caitanya appeared in order to taste the feelings Rādhārāṇī felt upon seeing Kṛṣṇa. 

Kṛṣṇa Himself could not understand the ecstatic feelings of Rādhārāṇī toward Him, and therefore He desired to accept the role of Rādhārāṇī and thereby taste these feelings. 

Lord Caitanya is Kṛṣṇa with the feelings of Rādhārāṇī; in other words, He is a combination of Rādhā and Kṛṣṇa. 

It is therefore said, śrī-kṛṣṇa-caitanya rādhā-kṛṣṇa nahe anya. By worshiping Śrī Caitanya Mahāprabhu alone, one can relish the loving affairs of Rādhā and Kṛṣṇa together. 

One should therefore try to understand Rādhā-Kṛṣṇa not directly but through Śrī Caitanya Mahāprabhu and through His devotees. 

Śrīla Narottama dāsa Ṭhākura therefore says, rūpa-raghunātha-pade haibe ākuti, kabe hāma bujhaba se yugala-pīriti- 

"When shall I develop a mentality of service toward Śrī Rūpa Gosvāmī, Sanātana Gosvāmī, Raghunātha dāsa Gosvāmī and the other devotees of Lord Caitanya and thus become eligible to understand the pastimes of Śrī Rādhā and Kṛṣṇa?"

As Caitanya Mahāprabhu, Kṛṣṇa Himself assumed the position of Śrīmatī Rādhārāṇī to taste Her ecstatic situation." (CC Adi 13.43, Purport).

Srila Prabhupada - "Among the gopīs, Śrīmatī Rādhikā (Radharani) is the foremost. She surpasses all in beauty, in good qualities, in good fortune and, above all, in love." (Caitanya Caritāmṛta Ādi 4.214)

Srila Prabhupada - "The beauty of Śrīmatī Rādhārāṇī’s eyes forcibly devours the beauty of newly grown blue lotus flowers, and the beauty of Her face surpasses that of an entire forest of fully blossomed lotuses. Her bodily luster seems to place even gold into a painful situation. Thus the wonderful, unprecedented beauty of Śrīmatī Rādhārāṇī is awakening in Vṛndāvana."(Caitanya Caritāmṛta Antya 1.169, Purport)

Srila Prabhupada - "The beauty of Śrīmatī Rādhārāṇī is described as follows: 'Her eyes defeat the attractive features of the eyes of the cakorī bird. When one sees the face of Rādhārāṇī, he immediately hates the beauty of the moon. Her bodily complexion defeats the beauty of gold. Thus, let us all look upon the transcendental beauty of Śrīmatī Rādhārāṇī." (Nectar of Devotion, Chapter 44)

Srila Prabhupada - "In the Vidagdha-mādhava, Second Act, verse 31, Kṛṣṇa tells His friend, 'My dear friend, what a wonderful thing it is that since I have seen the beautiful lotus eyes of Śrīmatī Rādhārāṇī, I have developed a tendency to spit on the moon and the lotus flower!"(Nectar of Devotion, Chapter 50)

Srila Prabhupada -"There is no comparison to Radharani's beauty and the luster of Her transcendental body. The so-called beauty of the moon has fallen on the ground in the presence of Radharani's beauty." (From Vrindavana by Srila Narottama das Thakura)

Srila Prabhupada - "Śrīmatī Rādhārāṇī’s affection, Her exquisite beauty and good behavior, Her artistic dancing and chanting and Her poetic compositions are all so attractive that they attract the mind of Kṛṣṇa, who attracts the mind of everyone in the universe."(Caitanya Caritāmṛta Madhya 17.212)

Srila Prabhupada - "Śrīla Rūpa Gosvāmī has stated that devotional service attracts even Kṛṣṇa. Kṛṣṇa attracts everyone, but devotional service attracts Kṛṣṇa. The symbol of devotional service in the highest degree is Rādhārāṇī. Kṛṣṇa is called Madana-mohana, which means that He is so attractive that He can defeat the attraction of thousands of Cupids. 

But Rādhārāṇī is still more attractive than Kṛṣṇa, for She can even attract Kṛṣṇa. Therefore, devotees call Her Madana mohana mohinī—the attractor of the attractor of Cupid." (Nectar of Devotion, Chapter 1)*^^*.