How do you simplify square root of 70 / square root of 40?

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How do you simplify square root of 70 / square root of 40?

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Answer 1 · 2015-09-19T01:18:10

$\frac{\sqrt{70}}{\sqrt{40}} = \frac{\sqrt{7}}{2}$ $sqrt(70) / sqrt(40) = sqrt(7)/2$

Explanation:

Using prime factorization, $\frac{\sqrt{70}}{\sqrt{40}}$ $sqrt(70) / sqrt(40)$ can be rewritten as $\frac{\sqrt{7 \cdot 5 \cdot 2}}{\sqrt{5 \cdot 2^{3}}}$ $sqrt(7*5*2) / sqrt(5*2^3$

$\sqrt{5 \cdot 2}$ $sqrt(5*2)$ is found in both the numerator and denominator and cancel each other out:

$\frac{\sqrt{7 \cdot 5 \cdot 2}}{\sqrt{5 \cdot 2^{3}}} = \frac{\sqrt{7}}{\sqrt{2^{2}}}$ $sqrt(7*5*2) / sqrt(5*2^3) = sqrt(7) / sqrt( 2^2)$

The denominator $\sqrt{2^{2}}$ $sqrt( 2^2)$ , or $\sqrt{4}$ $sqrt(4)$ , is a perfect square which simplifies to $2$ $2$ :

$\frac{\sqrt{7}}{\sqrt{2^{2}}} = \frac{\sqrt{7}}{2}$ $sqrt(7) / sqrt( 2^2) = sqrt(7)/2$

This is the simplified expression.

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How do you simplify square root of 70 / square root of 40?

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