Solve for x square root of 10x=3 square root of x+1

$\sqrt{10 x} = 3 \sqrt{x + 1}$

Step 1

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

${\sqrt{10 x}}^{2} = {(3 \sqrt{x + 1})}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 x}$ as ${(10 x)}^{\frac{1}{2}}$ .

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

Simplify the left side.

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

Multiply the exponents in ${({(10 x)}^{\frac{1}{2}})}^{2}$ .

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

${(10 x)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{x + 1})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(10 x)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{x + 1})}^{2}$

Rewrite the expression.

${(10 x)}^{1} = {(3 \sqrt{x + 1})}^{2}$

Simplify.

$10 x = {(3 \sqrt{x + 1})}^{2}$

Simplify the right side.

Simplify ${(3 \sqrt{x + 1})}^{2}$ .

Simplify the expression.

Apply the product rule to $3 \sqrt{x + 1}$ .

$10 x = 3^{2} {\sqrt{x + 1}}^{2}$

Raise $3$ to the power of $2$ .

$10 x = 9 {\sqrt{x + 1}}^{2}$

Rewrite ${\sqrt{x + 1}}^{2}$ as $x + 1$ .

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

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

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$10 x = 9 {(x + 1)}^{1}$

Simplify.

$10 x = 9 (x + 1)$

Apply the distributive property.

$10 x = 9 x + 9 \cdot 1$

Multiply $9$ by $1$ .

$10 x = 9 x + 9$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $9 x$ from both sides of the equation.

$10 x - 9 x = 9$

Subtract $9 x$ from $10 x$ .

$x = 9$

Solve for x square root of 10x=3 square root of x+1

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