Question

Rationlisw the demonitor of 5÷4root2+3root
3

Please answer with steps

Answer 1

HOLA..... (^_^)

5 / (4√2 + 3√3)

= [ 5/ (4√2 + 3√3) ] × [ ( 4√2 - 3√3 ) / (4√2 - 3√3) ]

= [ 5 × 4√2 - 5 × 3√3 ] / (4√2)^2 - (3√3)^2

= (20√2 - 15√3) / 32 - 27

= (20√2 - 15√3) / 5

Answer 2

Heya !!!

Here is your answer.

Given :
$\frac{5}{4 \sqrt{2} + 3 \sqrt{3} }$
Now, rationalize...

$\frac{5}{4 \sqrt{2} + 3 \sqrt{3} } \times \frac{4 \sqrt{2} - 3 \sqrt{3} }{4 \sqrt{2} - 3 \sqrt{3} } \\ = \frac{5(4 \sqrt{2} - 3 \sqrt{3}) }{{(4 \sqrt{2})}^{2} - {(3 \sqrt{3}) }^{2} } \\ = \frac{5(4 \sqrt{2} - 3\sqrt{3}) }{32 - 27} \\ = \frac{5(4 \sqrt{2} - 3\sqrt{3}) }{5} \\ = 4 \sqrt{2} - 3\sqrt{3}$
Hope It Helps