How do you rationalize the denominator and simplify $\frac{5}{\sqrt{14} - 2}$ $5 / ( sqrt 14 - 2 )$ ?

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Answer 1 · 2016-04-08T06:44:22

$\frac{\sqrt{14} + 2}{2} = \frac{\sqrt{14}}{2} + 1$ $(sqrt14 + 2)/2 = sqrt14/2 + 1$

By rationalizing a fraction, we mean removing any irrational values from the denominator, without changing the fraction.

Here, we have to remove $\sqrt{14}$ $sqrt14$ from the denominator, without changing the value of the expression.

We know that $a^{2} - b^{2} = (a + b) (a - b)$ $a^2-b^2 =(a+b)(a-b)$

We have $\sqrt{14} - 2$ $sqrt14-2$ as the denominator. To remove the square root, we must multiply the denominator by $\sqrt{14} + 2$ $sqrt14+2$

Dividing and multiplying a fraction by the same number does not change the fraction.

$\frac{5}{\sqrt{14} - 2} \times \frac{\sqrt{14} + 2}{\sqrt{14} + 2}$ $5/(sqrt14 -2) xx (sqrt14+2)/(sqrt14 + 2)$

$\frac{5 \times (\sqrt{14} + 2)}{(\sqrt{14} - 2) (\sqrt{14} + 2)}$ $(5 xx (sqrt14+2))/((sqrt14 -2)(sqrt14 + 2))$

$\frac{5 \sqrt{14} + 10}{{(\sqrt{14})}^{2} - 2^{2}}$ $(5sqrt14 + 10)/((sqrt14)^2 - 2^2)$

$\frac{5 \sqrt{14} + 10}{14 - 4} = \frac{5 \sqrt{14} + 10}{10}$ $(5sqrt14 + 10)/(14 -4) =(5sqrt14 + 10)/10$

5 is the common factor of the numerator.

$\frac{5 (\sqrt{14} + 2)}{10}$ $(5(sqrt14 + 2))/10$

Cancel 5 from the numerator and denominator.

$\frac{\sqrt{14} + 2}{2} = \frac{\sqrt{14}}{2} + 1$ $(sqrt14 + 2)/2 = sqrt14/2 + 1$

How do you rationalize the denominator and simplify 5√14−25 / ( sqrt 14 - 2 )?