How do you simplify $\frac{\sqrt{8}}{\sqrt{7}}$ $sqrt8/sqrt7$ ?

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How do you simplify $\frac{\sqrt{8}}{\sqrt{7}}$ $sqrt8/sqrt7$ ?

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Answer 1 · 2016-08-12T13:37:36

$\frac{2 \sqrt{14}}{7}$ $(2sqrt14)/7$

Explanation:

It is not good maths practice to leave a radical in the denominator.

We can "rationalize the denominator" which means changing it from an irrational to a rational number.

$\frac{\sqrt{8}}{\sqrt{7}} = \frac{\sqrt{8}}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} because \frac{\sqrt{7}}{\sqrt{7}} = 1$ $sqrt8/sqrt7 = sqrt8/sqrt7 xx sqrt7/sqrt7 " because "sqrt7/sqrt7 =1$

$\frac{\sqrt{8}}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{8 \times 7}}{7} {\sqrt{7}}^{2} = 7$ $sqrt8/sqrt7 xx sqrt7/sqrt7 = sqrt(8xx7)/7 " "sqrt7^2 =7$

= $\frac{\sqrt{2 \times 2 \times 2 \times 7}}{7}$ $sqrt(2xx2xx2xx7) /7$

= $\frac{2 \sqrt{14}}{7}$ $(2sqrt14)/7$

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How do you simplify $\frac{\sqrt{8}}{\sqrt{7}}$ $sqrt8/sqrt7$ ?

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