Solve n^2=2^5

$$n ^ { 2 } = 2 ^ { 5 }$$

Solve for n

$$n=4\sqrt{2}\approx 5.656854249$$

$$n=-4\sqrt{2}\approx -5.656854249$$

Steps by Finding Square Root

Calculate 2 to the power of 5 and get 32.

$$n^{2}=32$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 2 to the power of 5 and get 32.

$$n^{2}=32$$

Subtract 32 from both sides.

$$n^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-32\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-32\right)}}{2}$$

Multiply -4 times -32.

$$n=\frac{0±\sqrt{128}}{2}$$

Take the square root of 128.

$$n=\frac{0±8\sqrt{2}}{2}$$

Now solve the equation n=\frac{0±8\sqrt{2}}{2} when ± is plus.

$$n=4\sqrt{2}$$

Now solve the equation n=\frac{0±8\sqrt{2}}{2} when ± is minus.

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

The equation is now solved.

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