Solve by Factoring 90=9 square root of 25v

$90 = 9 \sqrt{25 v}$

Step 1

Subtract $9 \sqrt{25 v}$ from both sides of the equation.

$90 - 9 \sqrt{25 v} = 0$

Step 2

Simplify each term.

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

$90 - 9 \sqrt{5^{2} v} = 0$

Pull terms out from under the radical.

$90 - 9 (5 \sqrt{v}) = 0$

Multiply $5$ by $- 9$ .

$90 - 45 \sqrt{v} = 0$

Step 3

Factor $45$ out of $90 - 45 \sqrt{v}$ .

Factor $45$ out of $90$ .

$45 (2) - 45 \sqrt{v} = 0$

Factor $45$ out of $- 45 \sqrt{v}$ .

$45 (2) + 45 (- \sqrt{v}) = 0$

Factor $45$ out of $45 (2) + 45 (- \sqrt{v})$ .

$45 (2 - \sqrt{v}) = 0$

Step 4

Divide each term in $45 (2 - \sqrt{v}) = 0$ by $45$ and simplify.

Divide each term in $45 (2 - \sqrt{v}) = 0$ by $45$ .

$\frac{45 (2 - \sqrt{v})}{45} = \frac{0}{45}$

Simplify the left side.

Cancel the common factor of $45$ .

Cancel the common factor.

$\frac{45 (2 - \sqrt{v})}{45} = \frac{0}{45}$

Divide $2 - \sqrt{v}$ by $1$ .

$2 - \sqrt{v} = \frac{0}{45}$

Simplify the right side.

Divide $0$ by $45$ .

$2 - \sqrt{v} = 0$

Step 5

Subtract $2$ from both sides of the equation.

$- \sqrt{v} = - 2$

Step 6

To remove the radical on the left side of the equation, square both sides of the equation.

${(- \sqrt{v})}^{2} = {(- 2)}^{2}$

Step 7

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{v}$ as $v^{\frac{1}{2}}$ .

${(- v^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Simplify the left side.

Simplify ${(- v^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- v^{\frac{1}{2}}$ .

${(- 1)}^{2} {(v^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Raise $- 1$ to the power of $2$ .

$1 {(v^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Multiply ${(v^{\frac{1}{2}})}^{2}$ by $1$ .

${(v^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Multiply the exponents in ${(v^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$v^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$v^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Rewrite the expression.

$v^{1} = {(- 2)}^{2}$

Simplify.

$v = {(- 2)}^{2}$

Simplify the right side.

Raise $- 2$ to the power of $2$ .

$v = 4$

Solve by Factoring 90=9 square root of 25v

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