Question

$1\sqrt{7 + 2}$
​

Answer 1

Step-by-step explanation:

Rationalization

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

7

+2

1

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}}

3

7

+2