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Algebra Difficulty 1.9 Junior Find the answer

If 25n=3\sqrt{25-\sqrt{n}}=3, what is the value of nn?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since 25n=3\sqrt{25-\sqrt{n}}=3, then 25n=925-\sqrt{n}=9. Thus, n=16\sqrt{n}=16 and so n=162=256n=16^{2}=256.

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