Solve a^2=1152

$$a ^ { 2 } = 1152$$

Solve for a

$$a=24\sqrt{2}\approx 33.941125497$$

$$a=-24\sqrt{2}\approx -33.941125497$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$a=24\sqrt{2} a=-24\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 1152 from both sides.

$$a^{2}-1152=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1152 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-1152\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-1152\right)}}{2}$$

Multiply -4 times -1152.

$$a=\frac{0±\sqrt{4608}}{2}$$

Take the square root of 4608.

$$a=\frac{0±48\sqrt{2}}{2}$$

Now solve the equation a=\frac{0±48\sqrt{2}}{2} when ± is plus.

$$a=24\sqrt{2}$$

Now solve the equation a=\frac{0±48\sqrt{2}}{2} when ± is minus.

$$a=-24\sqrt{2}$$

The equation is now solved.

$$a=24\sqrt{2} a=-24\sqrt{2}$$