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Popular >

simplify sqrt(\sqrt{200)}

Solution

simplify

200

Solution

+1

Decimal Notation

3.76060 \dots

Solution steps

200

200 = 102

= 102

Apply radical rule:

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

102 = 102

= 102

Factor integer

10 = 2 \cdot 5

Apply radical rule:

2 \cdot 5 = 25

Apply exponent rule:

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

= 5 \cdot 2^{\frac{1}{2} + \frac{1}{4}}

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

= 5 \cdot 2^{\frac{3}{4}}

= 2^{\frac{3}{4}} 5

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt{200)} ?
The solution to sqrt(\sqrt{200)} is \sqrt[4]{2^3}sqrt(5)