Surd

$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}=a+b\sqrt{6}$, find $a \text{and} b$.

Write whether the pair of surds $5\sqrt{5}, \sqrt{75}$ are Like Surds or Unlike Surds.

If ${\left(\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}\right)}^2=3\sqrt{2}$ and ${\left(\sqrt{\mathrm{a}}-\sqrt{\mathrm{b}}\right)}^2=5\sqrt{2}$  Then find the value of  $8\sqrt{\mathrm{a}}\sqrt{\mathrm{b}}$.

If ${\left(\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}\right)}^2=16\sqrt{2}$ and ${\left(\sqrt{\mathrm{a}}-\sqrt{\mathrm{b}}\right)}^2=7\sqrt{2}$, Find the value of  $8\left(\mathrm{a}+\mathrm{b}\right)$.

The value of $\sqrt{\frac{(\sqrt{48} -\sqrt{32}) \left(\sqrt{3} - \sqrt{2}\right)}{10 + \sqrt{96}}}$ is:

Identify the expansion of the binomial surd $ (\sqrt{10}+\sqrt{2})(\sqrt{15}-\sqrt{3})$

to the mixed surd of the form $ p\sqrt{q}$.

Identify the surds in the expression $ 3\sqrt{75}-2\sqrt{48}$.

Find the conjugate of
$ -3+\sqrt{5}$.

Identify the smallest surd which is the rationalising factor of $ \sqrt{180}$.

If the product of two surds is a rational number then each of them is called the

Identify the rationalising factor of $ \nthroot{5}{{m}^{2}{n}^{3}{p}^{4}}$.

Which of the following is the same as 2$ \sqrt{2}$?

Which of the following is a group of like surds?

Which of the following is a pair of like surds?

Which of the following numbers is an irrational number, but NOT a surd?

Which of the following numbers is a surd?

Value of $\sqrt[4]{(81{)}^{-2}}$ is