How do you simplify $\frac{2}{\sqrt{7}}$ $2/sqrt7$ ?

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How do you simplify $\frac{2}{\sqrt{7}}$ $2/sqrt7$ ?

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Answer 1 · 2017-01-24T14:40:55

Multiply numerator and denominator by $\sqrt{7}$ $sqrt(7)$ :

Explanation:

$\frac{2}{\sqrt{7}} \cdot (\frac{\sqrt{7}}{\sqrt{7}})$ $2/(sqrt(7))*(sqrt(7)/sqrt(7))$ = $\frac{2 \sqrt{7}}{7}$ $(2sqrt(7))/7$ .
That is considered "rationalized" since the denominator is now a rational number, 7.

Example: Simplify $\frac{2}{3 \sqrt{12}}$ $2/(3sqrt(12))$

Simplify the denominator first, then rationalize.
$\frac{2}{3 \sqrt{4} \sqrt{3}}$ $2/(3sqrt(4)sqrt(3))$ = $\frac{2}{3 \cdot 2 \sqrt{3}}$ $2/(3*2sqrt(3))$ = $\frac{2}{6 \sqrt{3}}$ $2/(6sqrt(3))$

and reduce the $\frac{2}{6}$ $2/6$ = $\frac{1}{3 \sqrt{3}}$ $1/(3sqrt(3))$ .

NOW, multiply top and bottom by $\sqrt{3}$ $sqrt(3)$ :

$\frac{1}{3 \sqrt{3}} \cdot (\frac{\sqrt{3}}{\sqrt{3}})$ $1/(3sqrt(3))*(sqrt(3)/(sqrt(3)))$ = $\frac{\sqrt{3}}{3 \cdot 3}$ $(sqrt(3))/(3*3)$ = $\frac{\sqrt{3}}{9}$ $sqrt(3)/9$ .

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How do you simplify $\frac{2}{\sqrt{7}}$ $2/sqrt7$ ?

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