Question

simplify the following​

Answer 1

Answer:

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } = 1$

Step-by-step explanation:

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

Let us take conjugate (rationalise using denominator) for each term.

By rationalising the first term,

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{ \sqrt{10} - \sqrt{3} }{\sqrt{10} - \sqrt{3}}$

$\frac{7 \sqrt{30} - 21 }{7} = \sqrt{30} - 3$

By rationalising the second term,

$\frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6 } - \sqrt{5} }{ \sqrt{6 } - \sqrt{5}}$

$= \frac{2 \sqrt{30} - 10 }{1} = 2 \sqrt{30} - 10$

By rationalising the third term,

$\frac{3 \sqrt{ 2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3\sqrt{2} }{\sqrt{15} - 3\sqrt{2}}$

$= \frac{3 \sqrt{30} - 18}{ - 3} = 6 - \sqrt{30}$

By subtracting the three rationalised answers, we get the answer,

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

$= \sqrt{30} - 3 - (2 \sqrt{30} - 10) - (6 - \sqrt{30} )$

$=\sqrt{30} - 3 - 2 \sqrt{30} + 10 - 6 + \sqrt{30}$

$= 1$

Answer 2

HEY DEAR ❗❗

FIRST WE HAVE TO RATIONALISE EACH TERM SEPARATELY.

(IT WOULD BE EASY TO SOLVE).

THEN, ADD THEM UP TOGETHER,

AS YOU CAN SEE IN THE ATTACHED PIC.

❤Thank you❤

Hope it helps ❗❗

Mark as BRAINLIEST, I really need BRAINLIEST answers to reach next rank.