What is sqrt(\sqrt{40)} ?

The solution to sqrt(\sqrt{40)} is \sqrt[4]{2^3}\sqrt[4]{5}

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simplify sqrt(\sqrt{40)}

simplify

40

4 2^{3} 45

Decimal

2.51486 \dots

Solution steps

40

40 = 210

= 210

Apply radical rule:

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

210 = 210

= 210

10 = 410

= 2410

Factor integer

10 = 2 \cdot 5

= 2 4 2 \cdot 5

Apply radical rule:

n ab = n a n b

4 2 \cdot 5 = 4245

= 24245

Apply exponent rule:

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

242 = 2^{\frac{1}{2}} \cdot 2^{\frac{1}{4}} = 2^{\frac{1}{2} + \frac{1}{4}}

= 2^{\frac{1}{2} + \frac{1}{4}} 45

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

= 2^{\frac{3}{4}} 45

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

= 4 2^{3} 45

3 (\frac{1}{2})^{2}

3 x^{2} (5 x)

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

(t^{2} - 1)^{2}

re mainin g^{7}

What is sqrt(\sqrt{40)} ?
The solution to sqrt(\sqrt{40)} is \sqrt[4]{2^3}\sqrt[4]{5}