Question

rationalise the denominator 17/3/✓2+1​

Answer 1

Rationalization of denominator

♦ To rationalize the denominator we have to multiply the denominator and the numerator by the same number , which can make the denominator real

Now given number

$= \dfrac{17}{\dfrac{3}{\sqrt{2} + 1 }}$

$= \dfrac{17}{3\sqrt{2} + 3}$

No Rationalising

$= \dfrac{17}{3\sqrt{2} + 3} \times \dfrac{3\sqrt{2} - 3}{3\sqrt{2} - 3}$

$= \dfrac{17(3\sqrt{2} + 3)}{(3\sqrt{2})^2 - (3)^2} \\ \\ = \dfrac{51\sqrt{2} + 51}{(9)(2 ) - 9} \\\\ \dfrac{51\sqrt{2} + 51}{18 - 9} \\\\ \dfrac{51\sqrt{2} + 51}{9}$