Solve for u square root of 82u = square root of 79u+48

$\sqrt{82 u} = \sqrt{79 u + 48}$

Step 1

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

${\sqrt{82 u}}^{2} = {\sqrt{79 u + 48}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{82 u}$ as ${(82 u)}^{\frac{1}{2}}$ .

${({(82 u)}^{\frac{1}{2}})}^{2} = {\sqrt{79 u + 48}}^{2}$

Simplify the left side.

Simplify ${({(82 u)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(82 u)}^{\frac{1}{2}})}^{2}$ .

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

${(82 u)}^{\frac{1}{2} \cdot 2} = {\sqrt{79 u + 48}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(82 u)}^{\frac{1}{2} \cdot 2} = {\sqrt{79 u + 48}}^{2}$

Rewrite the expression.

${(82 u)}^{1} = {\sqrt{79 u + 48}}^{2}$

Simplify.

$82 u = {\sqrt{79 u + 48}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{79 u + 48}}^{2}$ as $79 u + 48$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{79 u + 48}$ as ${(79 u + 48)}^{\frac{1}{2}}$ .

$82 u = {({(79 u + 48)}^{\frac{1}{2}})}^{2}$

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

$82 u = {(79 u + 48)}^{\frac{1}{2} \cdot 2}$

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

$82 u = {(79 u + 48)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$82 u = {(79 u + 48)}^{\frac{2}{2}}$

Rewrite the expression.

$82 u = {(79 u + 48)}^{1}$

Simplify.

$82 u = 79 u + 48$

Step 3

Solve for $u$ .

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

Subtract $79 u$ from both sides of the equation.

$82 u - 79 u = 48$

Subtract $79 u$ from $82 u$ .

$3 u = 48$

Divide each term in $3 u = 48$ by $3$ and simplify.

Divide each term in $3 u = 48$ by $3$ .

$\frac{3 u}{3} = \frac{48}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 u}{3} = \frac{48}{3}$

Divide $u$ by $1$ .

$u = \frac{48}{3}$

Simplify the right side.

Divide $48$ by $3$ .

$u = 16$

Solve for u square root of 82u = square root of 79u+48

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