Solve for w square root of 5w+3 = square root of 4w+5

$\sqrt{5 w + 3} = \sqrt{4 w + 5}$

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

${\sqrt{5 w + 3}}^{2} = {\sqrt{4 w + 5}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 w + 3}$ as ${(5 w + 3)}^{\frac{1}{2}}$ .

${({(5 w + 3)}^{\frac{1}{2}})}^{2} = {\sqrt{4 w + 5}}^{2}$

Simplify the left side.

Simplify ${({(5 w + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 w + 3)}^{\frac{1}{2}})}^{2}$ .

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

${(5 w + 3)}^{\frac{1}{2} \cdot 2} = {\sqrt{4 w + 5}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 w + 3)}^{\frac{1}{2} \cdot 2} = {\sqrt{4 w + 5}}^{2}$

Rewrite the expression.

${(5 w + 3)}^{1} = {\sqrt{4 w + 5}}^{2}$

Simplify.

$5 w + 3 = {\sqrt{4 w + 5}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{4 w + 5}}^{2}$ as $4 w + 5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 w + 5}$ as ${(4 w + 5)}^{\frac{1}{2}}$ .

$5 w + 3 = {({(4 w + 5)}^{\frac{1}{2}})}^{2}$

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

$5 w + 3 = {(4 w + 5)}^{\frac{1}{2} \cdot 2}$

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

$5 w + 3 = {(4 w + 5)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5 w + 3 = {(4 w + 5)}^{\frac{2}{2}}$

Rewrite the expression.

$5 w + 3 = {(4 w + 5)}^{1}$

Simplify.

$5 w + 3 = 4 w + 5$

Solve for $w$ .

Move all terms containing $w$ to the left side of the equation.

Subtract $4 w$ from both sides of the equation.

$5 w + 3 - 4 w = 5$

Subtract $4 w$ from $5 w$ .

$w + 3 = 5$

Move all terms not containing $w$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$w = 5 - 3$

Subtract $3$ from $5$ .

$w = 2$