What is sqrt(10*\sqrt{5)} ?

The solution to sqrt(10*\sqrt{5)} is \sqrt[4]{5^3}sqrt(2)

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simplify sqrt(10*\sqrt{5)}

simplify

10 \cdot 5

Decimal Notation

4.72870 \dots

Solution steps

105

Apply radical rule:

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

105 = 105

= 105

Factor integer

10 = 5 \cdot 2

Apply radical rule:

5 \cdot 2 = 52

Apply exponent rule:

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

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

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

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

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

6 x^{2} + 13 x - 28

sin^{2} (x) + cos (2 x)

\frac{1}{x} \cdot 2

\frac{1}{x} \cdot 1

20 - 10 y - 7 y + 9

What is sqrt(10*\sqrt{5)} ?
The solution to sqrt(10*\sqrt{5)} is \sqrt[4]{5^3}sqrt(2)