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Popular >

simplify sqrt(\sqrt[3]{5^7)}

Solution

simplify

Solution

+1

Decimal Notation

6.53830 \dots

Solution steps

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

25 = 5

Apply radical rule:

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

Apply radical rule:

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

5^{\frac{1}{3}} = (5^{\frac{1}{3}})^{\frac{1}{2}}

= 5 (5^{\frac{1}{3}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(5^{\frac{1}{3}})^{\frac{1}{2}} = 5^{\frac{1}{3} \cdot \frac{1}{2}}

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

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

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

Apply exponent rule:

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt[3]{5^7)} ?
The solution to sqrt(\sqrt[3]{5^7)} is 5\sqrt[6]{5}