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Popular >

simplify \sqrt[8]{225^4}

Solution

simplify

Solution

15

Solution steps

Apply radical rule:

= (22 5^{4})^{\frac{1}{8}}

Apply exponent rule:

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

= 22 5^{4 \cdot \frac{1}{8}}

4 \cdot \frac{1}{8} = \frac{1}{2}

= 22 5^{\frac{1}{2}}

a^{\frac{1}{2}} = a

= 225

Factor the number:

225 = 1 5^{2}

= 1 5^{2}

Apply radical rule:

1 5^{2} = 15

= 15

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{225^4} ?
The solution to \sqrt[8]{225^4} is 15