Solve 1000=a*a*1

$$1000 = a \cdot a \cdot 1$$

Solve for a

$$a=10\sqrt{10}\approx 31.622776602$$

$$a=-10\sqrt{10}\approx -31.622776602$$

Steps by Finding Square Root

Multiply a and a to get a^{2}.

$$1000=a^{2}\times 1$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}\times 1=1000$$

Divide both sides by 1.

$$a^{2}=1000$$

Take the square root of both sides of the equation.

$$a=10\sqrt{10} a=-10\sqrt{10}$$

Steps Using the Quadratic Formula

Multiply a and a to get a^{2}.

$$1000=a^{2}\times 1$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}\times 1=1000$$

Subtract 1000 from both sides.

$$a^{2}\times 1-1000=0$$

Reorder the terms.

$$a^{2}-1000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-1000\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-1000\right)}}{2}$$

Multiply -4 times -1000.

$$a=\frac{0±\sqrt{4000}}{2}$$

Take the square root of 4000.

$$a=\frac{0±20\sqrt{10}}{2}$$

Now solve the equation a=\frac{0±20\sqrt{10}}{2} when ± is plus.

$$a=10\sqrt{10}$$

Now solve the equation a=\frac{0±20\sqrt{10}}{2} when ± is minus.

$$a=-10\sqrt{10}$$

The equation is now solved.

$$a=10\sqrt{10} a=-10\sqrt{10}$$