Question

rationalise the denomi
nator of root 6/root 3-root 2

Answer 1

6/root 3-root 2×root 3 + root 2/root3+root2
6root 3 + 6 root 2/ (root 3)vol square - (root2)vol square
6root3+ 6 root 2 / 3-2
6 root 3+ 6 root 2

Answer 2

Answer:

$\frac{\sqrt{6}}{\sqrt{3}-\sqrt{2}}=3\sqrt{2}+2\sqrt{3}$

Step-by-step explanation:

$Given \: \frac{\sqrt{6}}{\sqrt{3}-\sqrt{2}}$

$Rationalising\: factor\: of \\(\sqrt{3}-\sqrt{2}) \:is \:\\(\sqrt{3}+\sqrt{2})$

$=\frac{\sqrt{6}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}\\=\frac{\sqrt{6}(\sqrt{3}+\sqrt{2})}{(\sqrt{3})^{2}-(\sqrt{2})^{2})}\\=\frac{\sqrt{6}(\sqrt{3}+\sqrt{2})}{3-2}\\=\sqrt{6}\times \sqrt{3} +\sqrt{6}\times \sqrt{2}\\=3\sqrt{2}+2\sqrt{3}$

Therefore,

$\frac{\sqrt{6}}{\sqrt{3}-\sqrt{2}}=3\sqrt{2}+2\sqrt{3}$

•••♪