Question

5√7+2/5√7-2....... rationalize​

Answer 1

$\frac{(5\sqrt{7} + 2) }{(5\sqrt{7} - 2)} \\= \frac{(5\sqrt{7} + 2)(5\sqrt{7} +2) }{(5\sqrt{7} - 2)(5\sqrt{7} +2)} \\= \frac{(5\sqrt{7} + 2)^{2}}{(5\sqrt{7})^{2} - 2^{2}} \\= \frac{(5\sqrt{7})^{2} + 2^{2} + 2\times (5\sqrt{7} ) \times 2}{ 175 - 4 } \\= \frac{175 + 4+20\sqrt{7}}{171} \\= \frac{179+20\sqrt{7}}{171}$

Therefore.,

$\red{\frac{(5\sqrt{7} + 2) }{(5\sqrt{7} - 2)} }\\\green {= \frac{179+20\sqrt{7}}{171}}$

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