How do you simplify $\frac{\sqrt{2}}{\sqrt{10}}$ $sqrt 2 / sqrt 10$ ?

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How do you simplify $\frac{\sqrt{2}}{\sqrt{10}}$ $sqrt 2 / sqrt 10$ ?

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Answer 1 · 2017-08-14T08:30:50

$\frac{\sqrt{5}}{5}$ $sqrt5/5$

Explanation:

$to simplify a fraction with radicals we make the denominator$ $"to simplify a fraction with radicals we make the denominator"$
$rational, that is remove the radical$ $"rational, that is remove the radical"$

$using the laws of radicals$ $"using the "color(blue)"laws of radicals"$

$∙ x \sqrt{a} \times \sqrt{a} = a$ $•color(white)(x)sqrtaxxsqrta=a$

$∙ x \sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a} b$ $•color(white)(x)sqrtaxxsqrtbhArrsqrtab$

$to remove the radical from the denominator multiply the$ $"to remove the radical from the denominator multiply the"$
$numerator and denominator by \sqrt{10}$ $"numerator and denominator by "sqrt10$

$\frac{\sqrt{2}}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}}$ $sqrt2/sqrt10xxsqrt10/sqrt10$

$= \frac{\sqrt{2 \times 10}}{10}$ $=sqrt(2xx10)/10$

$= \frac{\sqrt{20}}{10} = \frac{\sqrt{4 \times 5}}{10} = \frac{\sqrt{4} \times \sqrt{5}}{10} = \frac{2 \sqrt{5}}{10} = \frac{\sqrt{5}}{5}$ $=sqrt20/10=sqrt(4xx5)/10=(sqrt4xxsqrt5)/10=(2sqrt5)/10=sqrt5/5$

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How do you simplify $\frac{\sqrt{2}}{\sqrt{10}}$ $sqrt 2 / sqrt 10$ ?

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