How do you simplify the square root of 40?

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Answer 1 · 2015-09-16T21:21:41

$2 \sqrt{10}$ $2sqrt10$

$\sqrt{40}$ $sqrt40$

Write the prime factors for $40$ $40$ .

$\sqrt{2 \times 2 \times 2 \times 5}$ $sqrt(2xx2xx2xx5)$

Group the same prime factors into pairs.

$\sqrt{(2 \times 2) \times 2 \times 5}$ $sqrt((2xx2)xx2xx5)$

Rewrite $(2 \times 2)$ $(2xx2)$ in exponent form.

$\sqrt{2^{2} \times 2 \times 5}$ $sqrt(2^2xx2xx5)$

Apply the rule $\sqrt{x^{2}} = x$ $sqrt(x^2)=x$

$\sqrt{2^{2}} = 2$ $sqrt(2^2)=2$

Simplify.

$2 \sqrt{2 \times 5}$ $2sqrt(2xx5)$

Simplify.

$2 \sqrt{10}$ $2sqrt10$