Question

Simplify by Ration ansing the
denominator
5+3 ✓2
_______
5-3 ✓2​

Answer 1

Answer:

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \\ \\ = \frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \times \frac{5 + 3 \sqrt{2} }{5 + 3 \sqrt{2} } \\ \\ = \frac{(5 + 3 \sqrt{2}) ^{2} }{ {5}^{2} - (3 \sqrt{2}) ^{2} } \\ \\ = \frac{ {5}^{2} + 2 \times 5 \times 3 \sqrt{2} + ({3 \sqrt{2} )}^{2} }{25 - 9 \times 2} \\ \\ = \frac{25 + 30 \sqrt{2} + 9 \times 2 }{25 - 18} \\ \\ = \frac{25 + 30 \sqrt{2} + 18}{25 - 18} \\ \\ = \frac{43 + 30 \sqrt{2} }{7}$

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Answer 2

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \times \frac{5 + 3 \sqrt{2} }{5 + 3 \sqrt{2} } \\ = \frac{ {(5 + 3 \sqrt{2} )}^{2} }{ {(5)}^{2} - {(3 \sqrt{2}) }^{2} } \\ = \frac{ {(5)}^{2} + {(3 \sqrt{2} ) }^{2} + 2(5)(3 \sqrt{2} )}{25 - (9)(2)} \\ = \frac{25 + 18 + 30 \sqrt{2} }{25 - 18} \\ = \frac{43 + 30 \sqrt{2} }{7}$

Since the question is about rationalising the denominator

It is completed

Bcoz in the denominator the no. is 7

and 7 is a rational no.