Question

17/3√2+1 rationalise the denominator

Answer 1

$\underline{\textsf{Given:}}$

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

$\underline{\textsf{To find:}}$

$\textsf{Rationalise denomintor of}$

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

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

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

$\textsf{To rationalize denominator multiply both numerator and}$

$\textsf{denominator by}\;\mathsf{3\sqrt{2}-1}}$

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

$\mathsf{=\dfrac{17(3\sqrt{2}-1)}{(3\sqrt{2})^2-1^2}}$

$\mathsf{=\dfrac{17(3\sqrt{2}-1)}{18-1}}$

$\mathsf{=\dfrac{17(3\sqrt{2}-1)}{17}}$

$\mathsf{=3\sqrt{2}-1}$

$\underline{\textsf{Answer:}}$

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