Solve for x square root of x=3 square root of 7

$\sqrt{x} = 3 \sqrt{7}$

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

${\sqrt{x}}^{2} = {(3 \sqrt{7})}^{2}$

Simplify each side of the equation.

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

${(x^{\frac{1}{2}})}^{2} = {(3 \sqrt{7})}^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = {(3 \sqrt{7})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(3 \sqrt{7})}^{2}$

Rewrite the expression.

$x^{1} = {(3 \sqrt{7})}^{2}$

Simplify.

$x = {(3 \sqrt{7})}^{2}$

Simplify the right side.

Simplify ${(3 \sqrt{7})}^{2}$ .

Simplify the expression.

Apply the product rule to $3 \sqrt{7}$ .

$x = 3^{2} {\sqrt{7}}^{2}$

Raise $3$ to the power of $2$ .

$x = 9 {\sqrt{7}}^{2}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$x = 9 {(7^{\frac{1}{2}})}^{2}$

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

$x = 9 \cdot 7^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x = 9 \cdot 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = 9 \cdot 7^{\frac{2}{2}}$

Rewrite the expression.

$x = 9 \cdot 7^{1}$

Evaluate the exponent.

$x = 9 \cdot 7$

Multiply $9$ by $7$ .

$x = 63$