Basic Math Examples

y^{2} = 63

$y^{2} = 63$

Step 1

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

y = \pm \sqrt{63}

$y = \pm \sqrt{63}$

Step 2

Simplify

\pm \sqrt{63}

$\pm \sqrt{63}$ .

Tap for more steps...

Step 2.1

Rewrite

63

$63$ as

3^{2} \cdot 7

$3^{2} \cdot 7$ .

Tap for more steps...

Step 2.1.1

Factor

9

$9$ out of

63

$63$ .

y = \pm \sqrt{9 (7)}

$y = \pm \sqrt{9 (7)}$

Step 2.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

y = \pm \sqrt{3^{2} \cdot 7}

$y = \pm \sqrt{3^{2} \cdot 7}$

y = \pm \sqrt{3^{2} \cdot 7}

$y = \pm \sqrt{3^{2} \cdot 7}$

Step 2.2

Pull terms out from under the radical.

y = \pm 3 \sqrt{7}

$y = \pm 3 \sqrt{7}$

y = \pm 3 \sqrt{7}

$y = \pm 3 \sqrt{7}$

Step 3

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

Tap for more steps...

Step 3.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

y = 3 \sqrt{7}

$y = 3 \sqrt{7}$

Step 3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

y = - 3 \sqrt{7}

$y = - 3 \sqrt{7}$

Step 3.3

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

y = 3 \sqrt{7}, - 3 \sqrt{7}

$y = 3 \sqrt{7}, - 3 \sqrt{7}$

y = 3 \sqrt{7}, - 3 \sqrt{7}

$y = 3 \sqrt{7}, - 3 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

y = 3 \sqrt{7}, - 3 \sqrt{7}

$y = 3 \sqrt{7}, - 3 \sqrt{7}$

Decimal Form:

y = 7.93725393 \dots, - 7.93725393 \dots

$y = 7.93725393 \dots, - 7.93725393 \dots$