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Popular >

simplify sqrt(2\sqrt{2)}

Solution

simplify

22

Solution

+1

Decimal Notation

1.68179 \dots

Solution steps

22

Apply radical rule:

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

22 = 22

= 22

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

= 2^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is sqrt(2\sqrt{2)} ?
The solution to sqrt(2\sqrt{2)} is \sqrt[4]{2^3}