Question

4. Rationalise the denominator 1/3+under root 2

Answer 1

$\sf{{\dfrac{1}{3 + {\sqrt{2}}}}}$


$\sf{\implies {\dfrac{1}{3 + {\sqrt{2}}}} × {\dfrac{3 - {\sqrt{2}}}{3 - {\sqrt{2}}}}}$


$\sf{\implies{\dfrac{(1)(3 - {\sqrt{2}})}{(3 + {\sqrt{2}})(3 - {\sqrt{2}})}}}$


${\boxed{\sf{(a + b )(a - b) = a^2 - b^2}}}$


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


$\sf{\implies {\dfrac{3 - {\sqrt{2}}}{9 - 2}}}$


$\sf\red{\implies {\dfrac{3 - {\sqrt{2}}}{7}}}$