Solve for x square root of 2x=4 square root of 5

$\sqrt{2 x} = 4 \sqrt{5}$

Step 1

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

${\sqrt{2 x}}^{2} = {(4 \sqrt{5})}^{2}$

Step 2

Simplify each side of the equation.

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

${({(2 x)}^{\frac{1}{2}})}^{2} = {(4 \sqrt{5})}^{2}$

Simplify the left side.

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

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

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

${(2 x)}^{\frac{1}{2} \cdot 2} = {(4 \sqrt{5})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x)}^{\frac{1}{2} \cdot 2} = {(4 \sqrt{5})}^{2}$

Rewrite the expression.

${(2 x)}^{1} = {(4 \sqrt{5})}^{2}$

Simplify.

$2 x = {(4 \sqrt{5})}^{2}$

Simplify the right side.

Simplify ${(4 \sqrt{5})}^{2}$ .

Simplify the expression.

Apply the product rule to $4 \sqrt{5}$ .

$2 x = 4^{2} {\sqrt{5}}^{2}$

Raise $4$ to the power of $2$ .

$2 x = 16 {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$2 x = 16 {(5^{\frac{1}{2}})}^{2}$

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

$2 x = 16 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$2 x = 16 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x = 16 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$2 x = 16 \cdot 5^{1}$

Evaluate the exponent.

$2 x = 16 \cdot 5$

Multiply $16$ by $5$ .

$2 x = 80$

Step 3

Divide each term in $2 x = 80$ by $2$ and simplify.

Divide each term in $2 x = 80$ by $2$ .

$\frac{2 x}{2} = \frac{80}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{80}{2}$

Divide $x$ by $1$ .

$x = \frac{80}{2}$

Simplify the right side.

Divide $80$ by $2$ .

$x = 40$

Solve for x square root of 2x=4 square root of 5

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