How do you rationalize the denominator and simplify $\frac{(\sqrt{7}) - (\sqrt{2})}{(\sqrt{7}) + (\sqrt{2})}$ $((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))$ ?

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How do you rationalize the denominator and simplify $\frac{(\sqrt{7}) - (\sqrt{2})}{(\sqrt{7}) + (\sqrt{2})}$ $((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))$ ?

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Answer 1 · 2016-04-29T16:22:29

$\frac{9 - 2 \sqrt{14}}{5}$ $(9-2sqrt(14))/5$

Explanation:

Given: $\frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} + \sqrt{2}}$ $" "color(brown)((sqrt(7)-sqrt(2))/(sqrt(7)+sqrt(2)))$

Trick is to use the scenario: $a^{2} - b^{2} = (a + b) (a - b)$ $" "a^2-b^2=(a+b)(a-b)$

Multiply by 1 but in the form $1 = \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}$ $color(blue)(1=(sqrt(7)-sqrt(2))/(sqrt(7)-sqrt(2)))$

$\frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} + \sqrt{2}} \times \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}$ $color(brown)((sqrt(7)-sqrt(2))/(sqrt(7)+sqrt(2)))color(blue)( xx (sqrt(7)-sqrt(2))/(sqrt(7)-sqrt(2)))$

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

$\frac{7 - 2 \sqrt{7} \sqrt{2} + 2}{7 - 2}$ $(7-2sqrt(7)sqrt(2)+2)/(7-2)$

$\frac{9 - 2 \sqrt{14}}{5}$ $(9-2sqrt(14))/5$

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How do you rationalize the denominator and simplify $\frac{(\sqrt{7}) - (\sqrt{2})}{(\sqrt{7}) + (\sqrt{2})}$ $((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))$ ?

1 Answer

Explanation:

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How do you rationalize the denominator and simplify ((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))(√7)−(√2)(√7)+(√2) ((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))?

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Explanation:

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How do you rationalize the denominator and simplify $\frac{(\sqrt{7}) - (\sqrt{2})}{(\sqrt{7}) + (\sqrt{2})}$ $((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))$ ?