Question

Find square root of $\sqrt{48}-\sqrt{45}$ is

Answer 1

Square root of $\sqrt{48}-\sqrt{45}$.

We know,

$$\begin{gathered} \sqrt{48}=4\sqrt{3} \\ \Rightarrow \sqrt{48}=4\times 1.732\left[\because \sqrt{3}=1.732\right] \\ \Rightarrow \sqrt{48}=6.928...\left(i\right) \end{gathered}$$

And,

$$\begin{gathered} \sqrt{45}=3\sqrt{5} \\ \Rightarrow \sqrt{45}=3\times 2.236\left[\because \sqrt{5}=2.236\right] \\ \Rightarrow \sqrt{45}=6.708...\left(ii\right) \end{gathered}$$

Subtract both $eq.\left(ii\right)$from $eq.\left(i\right)$:

$$\begin{gathered} \sqrt{48}-\sqrt{45}=6.928-6.708 \\ \Rightarrow \sqrt{48}-\sqrt{45}=0.22 \end{gathered}$$

Take square roots on both sides:

$$\begin{gathered} \sqrt{\left(\sqrt{48}-\sqrt{45}\right)}=\sqrt{0.22} \\ \Rightarrow \sqrt{\left(\sqrt{48}-\sqrt{45}\right)}=0.4690 \end{gathered}$$

Hence, the square root of $\sqrt{48}-\sqrt{45}$ is $0.4690$.