Question

What is $15$ divided by the square root of $2$?

Answer 1

Determine the value when $\mathbf{15}$ divided by the square root of $\mathbf{2}$:

When the denominator of an expression contains a term with a square root (or a number under a radical sign), the process of converting it to an equivalent expression whose denominator is a rational number is called rationalizing the denominator.

Multiply and divide by the square root of $2$:

$$\begin{gathered} \Rightarrow \frac{15}{\sqrt{2}}·\frac{\sqrt{2}}{\sqrt{2}}=\frac{15\sqrt{2}}{2} \\ =7.5\sqrt{2} \end{gathered}$$

The value of $\sqrt{2}$ is $1.414$.

$\begin{array}{rcl}7.5\times 1.414& =& 10.605\end{array}$

Hence, the value when $\mathbf{15}$ divided by the square root of $\mathbf{2}$ is $\mathbf{10}\mathbf{.}\mathbf{605}$.