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Popular >

simplify sqrt(\sqrt[3]{243)}

Solution

simplify

Solution

+1

Decimal Notation

2.49804 \dots

Solution steps

Apply radical rule:

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

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

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

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt[3]{243)} ?
The solution to sqrt(\sqrt[3]{243)} is \sqrt[6]{3^5}