Question

rationalize denominator 7/√2+5​

Answer 1

$\frac{7}{2 \: + \: \sqrt{5} }$

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• We have to solve it by rationalizing it's denomination.

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→ $\frac{7}{2 \: + \: \sqrt{5} }$

Rationalize it

→ $\frac{7}{2 \: + \: \sqrt{5} }$ × $\frac{2 \: - \: \sqrt{5} }{2 \: - \: \sqrt{5} }$

(a + b) (a - b) = a² - b²

→ $\frac{7(2 \: - \: \sqrt{5}) }{(2)^{2} \: - \: (\sqrt{5})^{2} }$

→ $\frac{14 \: - \: 7\sqrt{5} }{(2)^{2} \: - \: (\sqrt{5})^{2} }$

→ $\frac{14 \: - \: 7\sqrt{5}}{4 \: - \: 5 }$

→ $\frac{14 \: - \: 7\sqrt{5}}{ - \:1}$

→ $7\sqrt{5}\:-\:14$

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$7\sqrt{5}\:-\:14$

__________ [ ANSWER ]

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