Srimati Radharani is not a jiva-tattva (jiva-soul) expansion of Krsna like us, She is non-different from Krsna.

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. It is explained by the Gosvāmīs that Rādhārāṇī is the manifestation of the pleasure potency of the Supreme Personality of Godhead. When the Supreme Lord wants to derive transcendental pleasure, He has to create a woman from His internal potency and that women is Srimati Radharani." (SB, Canto 3 Ch 31 text 38, Purport)

Krsna divided Himself into "two" just so He could experience loving reciprocal exchanges with a women and gave Her the name Srimati Radharani. 

Love can never be experienced and realized with just one, there must be "two" - "Radha and Krsna." 

For even Krsna, love can never exist when there is just "one", there must "two," therefore Krsna divides Himself into two, Kṛṣṇa and His other half, the most attractive Srimati Radharani.

Also Krsna’s Visnu-tattva direct expansions like Balarama,  His first expansion, are also God.

Then there is His mysterious expansion Siva, who is neither Visnu-tattva or jiva-tattva (jiva-soul) who spends all of his time in the material world. 

Next is Kṛṣṇa's separated individual jiva-souls (jiva-tattva) expansions, who can only experience loving reciprocal exchanges in a "two-way" voluntary inter-relationship based on mutual returns and cooperation.

Krsna is likened to the original candle that lights all the other candles (Visnu-tattva) of the same luminosity.

Srila Prabhupada - "We have got the propensity to love. Love means somebody else. Love cannot be "one" or love cannot be executed 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 love." (Lecture SB, Canto 1 Ch 2 text 6, Delhi, Nov 12, 1973)

Srila Prabhupāda – "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." (Aug 9, 1976, Tehran)

Srila Prabhupada - "Love is reciprocal, voluntary, good exchange of feeling. Then there is love. Not by force! Krsna does not want to become a lover like that, ‘You love me, otherwise I shall kill you!" (Washington D.C. July 8, 1976)

Srila Prabhupada - "The impersonalist philosophy is oneness, so how there be love with just one? Is it possible? Have you got any such experience that love means one? No. Love means two. There must be two, the lover and the beloved. Kṛṣṇa is already lover. He loves you so much that He's trying to get you back. That is Kṛṣṇa's attempt. "Please, My dear boy, or My dear friend, My dear servant." (SB, Canto 2 Ch 1 text 3, Paris, June 12, 1974)

To experience loving exchanges and emotions with a women, Krsna divided Himself into two, Srimati Radharani and Krsna in two different spiritual bodies.

Krsna wanted to experience loving emotions and affection with a women, this is why He divided Himself into "two," just so He could experience those loving exchanges.

Caitanya Caritamrita - "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." (CC Adi 4.56)

Srila Prabhupada - "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. 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. 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. 

Impersonalists cannot understand this without the help of a mahā-bhāgavata (great pure) 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." (CC Adi 4.56, Purport)

Caitanya Caritamrita - "Among the gopīs, Śrīmatī Rādhikā is the foremost. She surpasses all in beauty, in good qualities, in good fortune and, above all, in love." (CC 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." (CC, 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." (NOD, Ch 44)

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." (CC, Madhya 17.212)

Caitanya Caritamrita - "Rādhikā is the transformation of Kṛṣṇa’s love. She is His internal energy called hlādinī." (CC, Adi 4.59)

Srila Prabhupada - "Srimati Radharani's mind, senses and body are steeped in love for Kṛṣṇa. She is Kṛṣṇa’s own energy, and She helps Him in His pastimes. Śrīmatī Rādhārāṇī is as fully spiritual as Kṛṣṇa. No one should consider Her to be material. 

She is definitely not like the conditioned souls, who have material bodies, gross and subtle, covered by material senses. She is all-spiritual, and both Her body and Her mind are of the same spiritual embodiment. Because Her body is spiritual, Her senses are also spiritual. Thus Her body, mind and senses fully shine in love of Kṛṣṇa. 

She is the personified hlādinī-śakti (the pleasure-giving energy of the Lord’s internal potency), and therefore She is the only source of enjoyment for Śrī Kṛṣṇa. Śrī Kṛṣṇa cannot enjoy anything that is internally different from Him. Therefore Rādhā and Śrī Kṛṣṇa are identical. 

The sandhinī portion of Śrī Kṛṣṇa’s internal potency has manifested the all-attractive form of Śrī Kṛṣṇa, and the same internal potency, in the hlādinī feature, has presented Śrīmatī Rādhārāṇī, who is the attraction for the all-attractive. No one can match Śrīmatī Rādhārāṇī in the transcendental pastimes of Śrī Kṛṣṇa." (CC, Adi 4.71 Purport)

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, for She can even attract Kṛṣṇa. Therefore, devotees call Her Madana-mohana-mohinī—the attractor of the attractor of Cupid." (NOD, Ch 1)

Srila Prabhupada - "Rādhārāṇī is the internal potency of Krsna, we are the marginal potency (individual jiva-souls). Of course, originally, in that sense, everything is Kṛṣṇa's expansion. Sarvaṁ khalv idaṁ brahma. But even then there are different expansions. That is the difference between Māyāvāda philosophy and Vaiṣṇava philosophy. Caitanya Mahāprabhu teaches acintya bhedābheda. We are always simultaneously one and different. Always. We should remember that, we are eternal expansion of Kṛṣṇa, we are expansion of Rādhā also because Rādhā is also expansion of Kṛṣṇa. But still, different. This is our philosophy- 

"One and different simultaneously, Acintya bhedābheda."

Caitanya Mahāprabhu's philosophy is "inconceivable simultaneously one and different". This is explained in the Seventh Chapter of Bhagavad-gītā. The energies and the energetic is the same. Śakti-śaktimator abheda. 

Just like sun and the sunshine, they are the same. There is no difference. But the molecules of the sunshine particles, that is not equal to the sun. These truths we shall always remember. Acintyāḥ khalu ye bhāvāḥ. Therefore these are inconceivable. 

We are simultaneously one with Kṛṣṇa and Rādhā, and at the same time different." (Lecture BG, Ch 4.5 Montreal, June 10, 1968)

Madhudviṣa Swami - "Śrīla Prabhupāda, you spoke of inferior energy and superior energy. Those are two general categories. Are there othern categories of energies besides that, and specifically how could we understand Śrīmatī Rādhārāṇī? Is She ...?"

Srila Prabhupāda - "She is spiritual energy non-different than Krsna, She is Kṛṣṇa."

Madhudviṣa Swami - "But is She jīva-soul or?"

Srila Prabhupada - "No, no, no, She is Kṛṣṇa. If everything is Kṛṣṇa, and Rādhārāṇī is not Kṛṣṇa, then what is that? No, She is Kṛṣṇa, She is the Kṛṣṇa's pleasure potency."

Madhudviṣa Swami- "She is not jīva-soul?"

Srila Prabhupada - "No, no, no. She is Kṛṣṇa. Kṛṣṇa divided Himself into two, His energy and Himself. That energy, original spiritual energy, is Rādhārāṇī, that is stated by Jīva Gosvāmī. Rādhā kṛṣṇa-praṇaya-vikṛtir hlādinī śaktir asmāt. When Kṛṣṇa wants pleasure, He cannot accept the inferior energy. The same superior energy, Kṛṣṇa, is divided into two. That is Rādhā and Kṛṣṇa. 

And again, when they unite, that is Caitanya Mahāprabhu. Divided, they are Rādhā and Kṛṣṇa, and united, Caitanya Mahāprabhu. Śrī kṛṣṇa caitanya rādhā-kṛṣṇa nahe anya. Anya means another. 

So Śrī Kṛṣṇa Caitanya is combination of Rādhā and Kṛṣṇa. And when they are divided into two, that is Rādhā and Kṛṣṇa. Rādhā kṛṣṇa praṇaya vikṛtir hlādinī śaktir asmād ekātmānāv api bhuvi purā deha-bhedaṁ gatau tau, śrī-caitanyākhyaṁ prakaṭam adhunā tad-dvayaṁ caikyam āptam [Cc. Ādi 1.5]. 

Śrī Caitanya Mahāprabhu is Rādhā-Kṛṣṇa combination. But He is playing the part of Rādhārāṇī to understand Kṛṣṇa. This is Caitanya Mahāprabhu." (Lecture SB, June 6th 1974 Melb Australia)×*×