What is (sqrt(125))^{1/3} ?

The solution to (sqrt(125))^{1/3} is 5^{1/2}

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simplify (sqrt(125))^{1/3}

simplify

(125)^{\frac{1}{3}}

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

Decimal Notation

2.23606 \dots

Solution steps

(125)^{\frac{1}{3}}

125 = 55

= (55)^{\frac{1}{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(55)^{\frac{1}{3}} = 5^{\frac{1}{3}} (5)^{\frac{1}{3}}

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

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

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

Apply exponent rule:

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

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

= 5^{\frac{1}{3} + \frac{1}{6}}

Join

\frac{1}{3} + \frac{1}{6} : \frac{1}{2}

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

(x^{\frac{1}{5}} \cdot y^{\frac{2}{9}}) (x^{\frac{1}{2}} \cdot y^{\frac{4}{9}})

\frac{1}{3} \cdot 3.14 \cdot 5^{2} \cdot 5