Question

one by root 7 minus 2​

Answer 1

Answer:

Rationalization

\bf{\frac{1}{{\sqrt{7}} + 2}}7+21

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

= \bf{\frac{1({\sqrt{7}} + 2)}{({\sqrt{7}} + 2)({\sqrt{7}} - 2)}}(7+2)(7−2)1(7+2)

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

= \bf{\frac{{\sqrt{7}} - 2}{[{\sqrt{(7)}}^{2} - {(2)}^{2}]}}[(7)2−(2)2]7−2

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

= \bf{\frac{{\sqrt{7}} + 2}{(7 - 4)}}(7−4)7+2

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

thus , after rationalising we will get :-

\boxed{\frac{{\sqrt{7}} + 2}{3}}37+2