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Popular >

simplify 3sqrt(\sqrt{125)}

Solution

simplify

3125

Solution

+1

Decimal Notation

10.03110 \dots

Solution steps

3125

125 = 55

= 355

Apply radical rule:

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

55 = 55

= 355

Apply radical rule:

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

5 = 5^{\frac{1}{2}}

Apply radical rule:

= 3 \cdot 5^{\frac{1}{2}} \cdot 5^{\frac{1}{4}}

Apply exponent rule:

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

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

= 3 \cdot 5^{\frac{1}{2} + \frac{1}{4}}

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

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

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Frequently Asked Questions (FAQ)

What is 3sqrt(\sqrt{125)} ?
The solution to 3sqrt(\sqrt{125)} is 3\sqrt[4]{5^3}