Solve the Rational Equation for x 10 square root of 9x=60

$10 \sqrt{9 x} = 60$

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

${(10 \sqrt{9 x})}^{2} = 60^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 x}$ as ${(9 x)}^{\frac{1}{2}}$ .

${(10 {(9 x)}^{\frac{1}{2}})}^{2} = 60^{2}$

Simplify the left side.

Simplify ${(10 {(9 x)}^{\frac{1}{2}})}^{2}$ .

Simplify the expression.

Apply the product rule to $9 x$ .

${(10 (9^{\frac{1}{2}} x^{\frac{1}{2}}))}^{2} = 60^{2}$

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

${(10 ({(3^{2})}^{\frac{1}{2}} x^{\frac{1}{2}}))}^{2} = 60^{2}$

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

${(10 (3^{2 (\frac{1}{2})} x^{\frac{1}{2}}))}^{2} = 60^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(10 (3^{2 (\frac{1}{2})} x^{\frac{1}{2}}))}^{2} = 60^{2}$

Rewrite the expression.

${(10 (3^{1} x^{\frac{1}{2}}))}^{2} = 60^{2}$

Evaluate the exponent.

${(10 (3 x^{\frac{1}{2}}))}^{2} = 60^{2}$

Multiply $3$ by $10$ .

${(30 x^{\frac{1}{2}})}^{2} = 60^{2}$

Apply the product rule to $30 x^{\frac{1}{2}}$ .

$30^{2} {(x^{\frac{1}{2}})}^{2} = 60^{2}$

Raise $30$ to the power of $2$ .

$900 {(x^{\frac{1}{2}})}^{2} = 60^{2}$

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

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

$900 x^{\frac{1}{2} \cdot 2} = 60^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$900 x^{\frac{1}{2} \cdot 2} = 60^{2}$

Rewrite the expression.

$900 x^{1} = 60^{2}$

Simplify.

$900 x = 60^{2}$

Simplify the right side.

Raise $60$ to the power of $2$ .

$900 x = 3600$

Divide each term in $900 x = 3600$ by $900$ and simplify.

Divide each term in $900 x = 3600$ by $900$ .

$\frac{900 x}{900} = \frac{3600}{900}$

Simplify the left side.

Cancel the common factor of $900$ .

Cancel the common factor.

$\frac{900 x}{900} = \frac{3600}{900}$

Divide $x$ by $1$ .

$x = \frac{3600}{900}$

Simplify the right side.

Divide $3600$ by $900$ .

$x = 4$

Solve the Rational Equation for x 10 square root of 9x=60

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