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Popular >

simplify \sqrt[5]{3125^2}

Solution

simplify

Solution

25

Solution steps

Apply radical rule:

= (312 5^{2})^{\frac{1}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 312 5^{2 \cdot \frac{1}{5}}

2 \cdot \frac{1}{5} = \frac{2}{5}

= 312 5^{\frac{2}{5}}

Factor the number:

3125 = 5^{5}

= (5^{5})^{\frac{2}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(5^{5})^{\frac{2}{5}} = 5^{5 \cdot \frac{2}{5}} = 5^{2}

= 5^{2}

Refine

= 25

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{3125^2} ?
The solution to \sqrt[5]{3125^2} is 25