Pre-Algebra Examples

$y^{2} = \frac{49}{4}$

Step 1

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

$y = \pm \sqrt{\frac{49}{4}}$

Step 2

Simplify $\pm \sqrt{\frac{49}{4}}$ .

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Step 2.1

Rewrite $\sqrt{\frac{49}{4}}$ as $\frac{\sqrt{49}}{\sqrt{4}}$ .

$y = \pm \frac{\sqrt{49}}{\sqrt{4}}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Rewrite $49$ as $7^{2}$ .

$y = \pm \frac{\sqrt{7^{2}}}{\sqrt{4}}$

Step 2.2.2

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

$y = \pm \frac{7}{\sqrt{4}}$

Step 2.3

Simplify the denominator.

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Step 2.3.1

Rewrite $4$ as $2^{2}$ .

$y = \pm \frac{7}{\sqrt{2^{2}}}$

Step 2.3.2

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

$y = \pm \frac{7}{2}$

Step 3

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

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Step 3.1

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

$y = \frac{7}{2}$

Step 3.2

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

$y = - \frac{7}{2}$

Step 3.3

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

$y = \frac{7}{2}, - \frac{7}{2}$