Solve for x 90=9 square root of 25x

$90 = 9 \sqrt{25 x}$

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

$9 \sqrt{25 x} = 90$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

Simplify the expression.

Apply the product rule to $25 x$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $5$ by $9$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$2025 x = 90^{2}$

Simplify the right side.

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

$2025 x = 8100$

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

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

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

Simplify the left side.

Cancel the common factor of $2025$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $8100$ by $2025$ .

$x = 4$

Solve for x 90=9 square root of 25x

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