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

$2 y^{2} = 100$

Step 1

Divide each term in $2 y^{2} = 100$ by $2$ and simplify.

Divide each term in $2 y^{2} = 100$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y^{2}$ by $1$ .

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

Simplify the right side.

Divide $100$ by $2$ .

$y^{2} = 50$

Step 2

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

$y = \pm \sqrt{50}$

Step 3

Simplify $\pm \sqrt{50}$ .

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$y = \pm \sqrt{25 (2)}$

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

$y = \pm \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$y = \pm 5 \sqrt{2}$

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.

$y = 5 \sqrt{2}$

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

$y = - 5 \sqrt{2}$

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

$y = 5 \sqrt{2}, - 5 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = 5 \sqrt{2}, - 5 \sqrt{2}$

Decimal Form:

$y = 7.07106781 \dots, - 7.07106781 \dots$