Question

Rationalise the following
3-2root2/3+2root2​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} }$

Step by step explanation:

1. Here ,to rationalise first we check the denominator value and then we will multiply to both numerator and denominator with the opposite sign of Denominator.e.g.,=> 3+√2 opposite sign =>3-√2.

$\sf \longmapsto \dfrac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \times \dfrac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} }$

Identity used here :-

(a-b)²=a²+b²-2ab

(a+b)(a-b)=a²-b²

$\sf \longmapsto \dfrac{ {(3 - 2 \sqrt{2} )}^{2} }{ {(3)}^{2} - {(2 \sqrt{2}) }^{2} }$

$\sf \longmapsto \dfrac{ {(3)}^{2} + {(2 \sqrt{2} )}^{2} - 2(3)(2 \sqrt{2} ) }{9 - 8}$

$\sf \longmapsto \dfrac{9 + 8 - 12 \sqrt{2} }{1}$

$\sf \longmapsto \bold{17 - 12 \sqrt{2} }$

Extra information=>

Rationalising means removing root values from the denominator and shifts towards numerator side.

Answer 2

Answer:

Step-by-step explanation:

Here, to rationalise first we check the denominator value and then we will multiply to both the numerator and denominator with the opposite sign of the Denominator. e.g.,=> 3+√2 opposite sign =>3-√2.

The identity used here:-

(a-b)²=a²+b²-2ab

(a+b)(a-b)=a²-b²