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Popular >

simplify sqrt(7\sqrt{7)}

Solution

simplify

77

Solution

+1

Decimal Notation

4.30351 \dots

Solution steps

77

Apply radical rule:

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

77 = 77

= 77

Apply radical rule:

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

7 = 7^{\frac{1}{2}}

Apply radical rule:

= 7^{\frac{1}{2}} \cdot 7^{\frac{1}{4}}

Apply exponent rule:

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

7^{\frac{1}{2}} \cdot 7^{\frac{1}{4}} = 7^{\frac{1}{2} + \frac{1}{4}}

= 7^{\frac{1}{2} + \frac{1}{4}}

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

= 7^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is sqrt(7\sqrt{7)} ?
The solution to sqrt(7\sqrt{7)} is \sqrt[4]{7^3}