Solve sqrt{64n^2}=sqrt{8n^2}

$$\sqrt { 64 n ^ { 2 } } = \sqrt { 8 n ^ { 2 } }$$

Solve for n

$$n=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{64n^{2}}\right)^{2}=\left(\sqrt{8n^{2}}\right)^{2}$$

Calculate \sqrt{64n^{2}} to the power of 2 and get 64n^{2}.

$$64n^{2}=\left(\sqrt{8n^{2}}\right)^{2}$$

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

$$64n^{2}=8n^{2}$$

Subtract 8n^{2} from both sides.

$$64n^{2}-8n^{2}=0$$

Combine 64n^{2} and -8n^{2} to get 56n^{2}.

$$56n^{2}=0$$

Divide both sides by 56. Zero divided by any non-zero number gives zero.

$$n^{2}=0$$

Take the square root of both sides of the equation.

$$n=0 n=0$$

The equation is now solved. Solutions are the same.

$$n=0$$

Substitute 0 for n in the equation \sqrt{64n^{2}}=\sqrt{8n^{2}}.

$$\sqrt{64\times 0^{2}}=\sqrt{8\times 0^{2}}$$

Simplify. The value n=0 satisfies the equation.

$$0=0$$

Equation \sqrt{64n^{2}}=\sqrt{8n^{2}} has a unique solution.

$$n=0$$