Solve sqrt{100}=1/a^2

$$\sqrt { 100 } = \frac { 1 } { a ^ { 2 } }$$

Solve for a

$$a=\frac{\sqrt{10}}{10}\approx 0.316227766$$

$$a=-\frac{\sqrt{10}}{10}\approx -0.316227766$$

Steps by Finding Square Root

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a^{2}.

$$a^{2}\sqrt{100}=1$$

Calculate the square root of 100 and get 10.

$$a^{2}\times 10=1$$

Divide both sides by 10.

$$a^{2}=\frac{1}{10}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a^{2}.

$$a^{2}\sqrt{100}=1$$

Calculate the square root of 100 and get 10.

$$a^{2}\times 10=1$$

Subtract 1 from both sides.

$$a^{2}\times 10-1=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$10a^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 10\left(-1\right)}}{2\times 10}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 10\left(-1\right)}}{2\times 10}$$

Multiply -4 times 10.

$$a=\frac{0±\sqrt{-40\left(-1\right)}}{2\times 10}$$

Multiply -40 times -1.

$$a=\frac{0±\sqrt{40}}{2\times 10}$$

Take the square root of 40.

$$a=\frac{0±2\sqrt{10}}{2\times 10}$$

Multiply 2 times 10.

$$a=\frac{0±2\sqrt{10}}{20}$$

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

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

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

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

The equation is now solved.

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