Solve for v 90=9 square root of 25v

$90 = 9 \sqrt{25 v}$

Step 1

Rewrite the equation as $9 \sqrt{25 v} = 90$ .

$9 \sqrt{25 v} = 90$

Step 2

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

${(9 \sqrt{25 v})}^{2} = 90^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{25 v}$ as ${(25 v)}^{\frac{1}{2}}$ .

${(9 {(25 v)}^{\frac{1}{2}})}^{2} = 90^{2}$

Simplify the left side.

Simplify ${(9 {(25 v)}^{\frac{1}{2}})}^{2}$ .

Simplify the expression.

Apply the product rule to $25 v$ .

${(9 (25^{\frac{1}{2}} v^{\frac{1}{2}}))}^{2} = 90^{2}$

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

${(9 ({(5^{2})}^{\frac{1}{2}} v^{\frac{1}{2}}))}^{2} = 90^{2}$

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

${(9 (5^{2 (\frac{1}{2})} v^{\frac{1}{2}}))}^{2} = 90^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9 (5^{2 (\frac{1}{2})} v^{\frac{1}{2}}))}^{2} = 90^{2}$

Rewrite the expression.

${(9 (5^{1} v^{\frac{1}{2}}))}^{2} = 90^{2}$

Evaluate the exponent.

${(9 (5 v^{\frac{1}{2}}))}^{2} = 90^{2}$

Multiply $5$ by $9$ .

${(45 v^{\frac{1}{2}})}^{2} = 90^{2}$

Apply the product rule to $45 v^{\frac{1}{2}}$ .

$45^{2} {(v^{\frac{1}{2}})}^{2} = 90^{2}$

Raise $45$ to the power of $2$ .

$2025 {(v^{\frac{1}{2}})}^{2} = 90^{2}$

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

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

$2025 v^{\frac{1}{2} \cdot 2} = 90^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2025 v^{\frac{1}{2} \cdot 2} = 90^{2}$

Rewrite the expression.

$2025 v^{1} = 90^{2}$

Simplify.

$2025 v = 90^{2}$

Simplify the right side.

Raise $90$ to the power of $2$ .

$2025 v = 8100$

Step 4

Divide each term in $2025 v = 8100$ by $2025$ and simplify.

Divide each term in $2025 v = 8100$ by $2025$ .

$\frac{2025 v}{2025} = \frac{8100}{2025}$

Simplify the left side.

Cancel the common factor of $2025$ .

Cancel the common factor.

$\frac{2025 v}{2025} = \frac{8100}{2025}$

Divide $v$ by $1$ .

$v = \frac{8100}{2025}$

Simplify the right side.

Divide $8100$ by $2025$ .

$v = 4$

Solve for v 90=9 square root of 25v

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