Question

simplify the following by rationalising the denominator 7√3 - 5√2 / √48 + √18

Answer 1

Heya !!

Identity used :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$


$\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{2 \times 2 \times 2 \times 2 \times 3} + \sqrt{3 \times 3 \times 2} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{2 \times 2 \sqrt{3} + 3 \sqrt{2} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} }$

On rationalizing the denominator we get,

$= \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ = \frac{7 \sqrt{3}(4 \sqrt{3} - 3 \sqrt{2} ) - 5 \sqrt{2}(4 \sqrt{3} - 3 \sqrt{2} ) }{ {(4 \sqrt{3} )}^{2} - {(3 \sqrt{2} )}^{2} } \\ \\ = \frac{84 - 21 \sqrt{6} - 20 \sqrt{6} + 30}{48 - 18} \\ \\ = \frac{114 - 41 \sqrt{6} }{30} \\ \\ =$

Hope this helps ☺

Answer 2

Hey !!!!! Your answer =>

Refer to the attached file ^^^

Hope it will help you ☆▪☆ Thanks ^_^

☆ Be Brainly ☆