Solve sqrt{3n+12}=sqrt{n+8}

$$\sqrt { 3 n + 12 } = \sqrt { n + 8 }$$

Solve for n

$$n=-2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3n+12}\right)^{2}=\left(\sqrt{n+8}\right)^{2}$$

Calculate \sqrt{3n+12} to the power of 2 and get 3n+12.

$$3n+12=\left(\sqrt{n+8}\right)^{2}$$

Calculate \sqrt{n+8} to the power of 2 and get n+8.

$$3n+12=n+8$$

Subtract n from both sides.

$$3n+12-n=8$$

Combine 3n and -n to get 2n.

$$2n+12=8$$

Subtract 12 from both sides.

$$2n=8-12$$

Subtract 12 from 8 to get -4.

$$2n=-4$$

Divide both sides by 2.

$$n=\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$n=-2$$

Substitute -2 for n in the equation \sqrt{3n+12}=\sqrt{n+8}.

$$\sqrt{3\left(-2\right)+12}=\sqrt{-2+8}$$

Simplify. The value n=-2 satisfies the equation.

$$6^{\frac{1}{2}}=6^{\frac{1}{2}}$$

Equation \sqrt{3n+12}=\sqrt{n+8} has a unique solution.

$$n=-2$$