Solve Using the Square Root Property y^2=4/100

$y^{2} = \frac{4}{100}$

Step 1

Reduce the expression $\frac{4}{100}$ by cancelling the common factors.

Factor $4$ out of $4$ .

$y^{2} = \frac{4 (1)}{100}$

Factor $4$ out of $100$ .

$y^{2} = \frac{4 \cdot 1}{4 \cdot 25}$

Cancel the common factor.

$y^{2} = \frac{4 \cdot 1}{4 \cdot 25}$

Rewrite the expression.

$y^{2} = \frac{1}{25}$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{\frac{1}{25}}$

Step 3

Simplify $\pm \sqrt{\frac{1}{25}}$ .

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$y = \pm \frac{\sqrt{1}}{\sqrt{25}}$

Any root of $1$ is $1$ .

$y = \pm \frac{1}{\sqrt{25}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$y = \pm \frac{1}{\sqrt{5^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm \frac{1}{5}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{1}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{1}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{1}{5}, - \frac{1}{5}$