Solve n^2=46

$$n ^ { 2 } = 46$$

Solve for n

$$n=\sqrt{46}\approx 6.782329983$$

$$n=-\sqrt{46}\approx -6.782329983$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$n=\sqrt{46} n=-\sqrt{46}$$

Steps Using the Quadratic Formula

Subtract 46 from both sides.

$$n^{2}-46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-46\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-46\right)}}{2}$$

Multiply -4 times -46.

$$n=\frac{0±\sqrt{184}}{2}$$

Take the square root of 184.

$$n=\frac{0±2\sqrt{46}}{2}$$

Now solve the equation n=\frac{0±2\sqrt{46}}{2} when ± is plus.

$$n=\sqrt{46}$$

Now solve the equation n=\frac{0±2\sqrt{46}}{2} when ± is minus.

$$n=-\sqrt{46}$$

The equation is now solved.

$$n=\sqrt{46} n=-\sqrt{46}$$