Question

Solve the given equation and check the solution.

$\sqrt{10x}=20$

Short answer

The solution of$\sqrt{10x}=20$ is 40.

Step-by-step solution

Step 1. State the concept of ‘square of a square root’.

When the square root of a term is squared, then the resulting value will be the term which is inside the root. That is,

${\left(\sqrt{a}\right)}^2=a$

Step 2. Find the value of ‘x’.

Solve the equation$\sqrt{10x}=20$ to get the value of ‘x’.

$\sqrt{10x}=20$

Squaring both the sides

$$\begin{gathered} {\left(\sqrt{10x}\right)}^2={\left(20\right)}^2 \\ 10x=400\left[\text{Using\hspace{0.17em}\hspace{0.17em}}{\left(\sqrt{a}\right)}^2=a\right] \\ \frac{10x}{10}=\frac{400}{10} \\ x=40 \end{gathered}$$

Step 3. Verify the solution.

Substitute$x=40$ in the left hand side (L.H.S) of the equation $\sqrt{10x}=20$to verify whether the value satisfies the equation or not.

$$\begin{gathered} \text{L.H.S}=\sqrt{10x} \\ =\sqrt{10\left(40\right)} \\ =\sqrt{400} \\ =20 \\ =\text{R.H.S\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left[\text{R.H.S=Right\hspace{0.17em}\hspace{0.17em}hand\hspace{0.17em}\hspace{0.17em}side}\right] \end{gathered}$$

L.H.S=R.H.S

Thus,$x=40$satisfies the given equation.

Hence verified.