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Popular >

simplify sqrt(6*\sqrt{6)}

Solution

simplify

6 \cdot 6

Solution

+1

Decimal Notation

3.83365 \dots

Solution steps

66

Apply radical rule:

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

66 = 66

= 66

Apply radical rule:

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

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

Apply radical rule:

= 6^{\frac{1}{2}} \cdot 6^{\frac{1}{4}}

Apply exponent rule:

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

6^{\frac{1}{2}} \cdot 6^{\frac{1}{4}} = 6^{\frac{1}{2} + \frac{1}{4}}

= 6^{\frac{1}{2} + \frac{1}{4}}

\frac{1}{2} + \frac{1}{4} = \frac{3}{4}

= 6^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is sqrt(6*\sqrt{6)} ?
The solution to sqrt(6*\sqrt{6)} is \sqrt[4]{6^3}