Question

Rationalise the denominator 1/root 7-2

Answer 1

Hey friend!

Here's your answer

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$1 \div \sqrt{7 - 2 } \\ rationalising \: the \: denominator$
1/√7-2 x √7+2 /√7+2

= √7+2 / (√7)²-(2)²

= √7+2 / 7-4

= √7+2/ 3 is the answer.

# Hope it helps #

Answer 2

$\textbf{\underline{Rationalization}}$

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

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

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

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

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

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

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

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

thus , after rationalising we will get :-

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