Solve for x square root of x=1/7

$\sqrt{x} = \frac{1}{7}$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = {(\frac{1}{7})}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = {(\frac{1}{7})}^{2}$

Simplify the left side.

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = {(\frac{1}{7})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(\frac{1}{7})}^{2}$

Rewrite the expression.

$x^{1} = {(\frac{1}{7})}^{2}$

Simplify.

$x = {(\frac{1}{7})}^{2}$

Simplify the right side.

Simplify ${(\frac{1}{7})}^{2}$ .

Apply the product rule to $\frac{1}{7}$ .

$x = \frac{1^{2}}{7^{2}}$

One to any power is one.

$x = \frac{1}{7^{2}}$

Raise $7$ to the power of $2$ .

$x = \frac{1}{49}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{49}$

Decimal Form:

$x = 0.02040816 \dots$