Maharashtra Board Solutions for Chapter: Real Numbers, Exercise 3: Practice set

State the order of the surd $\sqrt[3]{18}$.

Simplify the following surd and write the value of $k$.

$\sqrt{27}=3\sqrt{k}$

If the simplest form of the surd $\sqrt{50}$ is of the form $a\sqrt{b}$, then find the value of $\left(a+b\right)$.

If the simplified form of the surd $\sqrt{250}$ is of the form $a\sqrt{b}$, then find the value of $\left(a+b\right)$

If the simplified form of the surd $\sqrt{112}$ is of the form $a\sqrt{b}$, then find the value of $\left(a+b\right)$

If the simplest form of $\sqrt{168}$ is $2\sqrt{k}$, then find the value of $k$.

Rationalize the denominator.

$\frac{6}{9\sqrt{3}}$

Rationalize the denominator.

$\frac{11}{\sqrt{3}}$