Simplify ( square root of 4x)^2

${(\sqrt{4 x})}^{2}$

Rewrite $4$ as $2^{2}$ .

${\sqrt{2^{2} x}}^{2}$

Pull terms out from under the radical.

${(2 \sqrt{x})}^{2}$

Simplify the expression.

Apply the product rule to $2 \sqrt{x}$ .

$2^{2} {\sqrt{x}}^{2}$

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

$4 {\sqrt{x}}^{2}$

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

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

$4 {(x^{\frac{1}{2}})}^{2}$

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

$4 x^{\frac{1}{2} \cdot 2}$

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

$4 x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 x^{\frac{2}{2}}$

Rewrite the expression.

$4 x^{1}$

Simplify.

$4 x$