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Popular >

simplify \sqrt[6]{125^3}

Solution

simplify

Solution

55

+1

Decimal Notation

11.18033 \dots

Solution steps

Apply radical rule:

= (12 5^{3})^{\frac{1}{6}}

Apply exponent rule:

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

= 12 5^{3 \cdot \frac{1}{6}}

3 \cdot \frac{1}{6} = \frac{1}{2}

= 12 5^{\frac{1}{2}}

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

= 125

Prime factorization of

125 : 5^{3}

= 5^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 5^{2} \cdot 5

Apply radical rule:

= 5 5^{2}

Apply radical rule:

5^{2} = 5

= 55

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Frequently Asked Questions (FAQ)

What is \sqrt[6]{125^3} ?
The solution to \sqrt[6]{125^3} is 5sqrt(5)