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Popular >

simplify \sqrt[3]{sqrt(192)}

Solution

simplify

Solution

+1

Decimal Notation

2.40187 \dots

Solution steps

192 = 83

Apply radical rule:

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{sqrt(192)} ?
The solution to \sqrt[3]{sqrt(192)} is 2\sqrt[6]{3}