Solve for l 90=l^2

$90 = l^{2}$

Step 1

Rewrite the equation as $l^{2} = 90$ .

$l^{2} = 90$

Step 2

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

$l = \pm \sqrt{90}$

Step 3

Simplify $\pm \sqrt{90}$ .

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$l = \pm \sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

$l = \pm \sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$l = \pm 3 \sqrt{10}$

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.

$l = 3 \sqrt{10}$

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

$l = - 3 \sqrt{10}$

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

$l = 3 \sqrt{10}, - 3 \sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$l = 3 \sqrt{10}, - 3 \sqrt{10}$

Decimal Form:

$l = 9.48683298 \dots, - 9.48683298 \dots$