Question

rationalize the denominator 2√7+√2/2√7-√2​

Answer 1

Answer:

see open this photo your answer

Answer 2

Rationalization:-

$\sf{\frac{1}{{\sqrt{7}} + 2}}$

firstly, change the sign of the denominator , i.e √7 - √2 will become √7 + 2 , so multiply this term both with numerator and denominator.

$= \sf{\frac{1({\sqrt{7}} + 2)}{({\sqrt{7}} + 2)({\sqrt{7}} - 2)}}$

Multiply the terms , and we know that (a+b)(a-b) = a² - b² , use this identity for denominator!

$= \sf{\frac{{\sqrt{7}} - 2}{[{\sqrt{(7)}}^{2} - {(2)}^{2}]}}$

Solve it more , square root and square will cancel out!

$= \sf{\frac{{\sqrt{7}} + 2}{(7 - 4)}}$

$= \sf{\frac{{\sqrt{7}} +2}{(3)}}$

thus , after rationalising we will get :-

$\underbrace {\overbrace{\frac{{\sqrt{7}} + 2}{3}}}$