What is sqrt(5\times \sqrt{5)} ?

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

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simplify sqrt(5\times \sqrt{5)}

simplify

5 \cdot 5

Decimal Notation

3.34370 \dots

Solution steps

55

Apply radical rule:

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

55 = 55

= 55

Apply radical rule:

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

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

Apply radical rule:

= 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}}

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

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

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

- 8 \times (- 2)

t^{3} - 3 t

0.85 m x y - \frac{1}{2} m x y

6 x^{2} - 13 x - 8

4 \times (- 8)

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