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Popular >

simplify sqrt(\sqrt{100)}

Solution

simplify

100

Solution

10

+1

Decimal Notation

3.16227 \dots

Solution steps

100

Apply radical rule:

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

= (10 0^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 10 0^{\frac{1}{2} \cdot \frac{1}{2}}

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

= 10 0^{\frac{1}{4}}

Factor the number:

100 = 1 0^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 10

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt{100)} ?
The solution to sqrt(\sqrt{100)} is square root of 10