Algebra Examples

$\frac{\sqrt{a}}{\sqrt{b}} = x$

Step 1

Cross multiply.

Tap for more steps...

Step 1.1

Cross multiply by setting the product of the numerator of the right side and the denominator of the left side equal to the product of the numerator of the left side and the denominator of the right side.

$x \cdot (\sqrt{b}) = \sqrt{a}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Multiply $x$ by $\sqrt{b}$ .

$x \sqrt{b} = \sqrt{a}$

Step 2

Rewrite the equation as $\sqrt{a} = x \sqrt{b}$ .

$\sqrt{a} = x \sqrt{b}$

Step 3

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

${\sqrt{a}}^{2} = {(x \sqrt{b})}^{2}$

Step 4

Simplify each side of the equation.

Tap for more steps...

Step 4.1

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

${(a^{\frac{1}{2}})}^{2} = {(x \sqrt{b})}^{2}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

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

Tap for more steps...

Step 4.2.1.1

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

Tap for more steps...

Step 4.2.1.1.1

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

$a^{\frac{1}{2} \cdot 2} = {(x \sqrt{b})}^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1.2.1

Cancel the common factor.

$a^{\frac{1}{2} \cdot 2} = {(x \sqrt{b})}^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

$a^{1} = {(x \sqrt{b})}^{2}$

Step 4.2.1.2

Simplify.

$a = {(x \sqrt{b})}^{2}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Simplify ${(x \sqrt{b})}^{2}$ .

Tap for more steps...

Step 4.3.1.1

Apply the product rule to $x \sqrt{b}$ .

$a = x^{2} {\sqrt{b}}^{2}$

Step 4.3.1.2

Rewrite ${\sqrt{b}}^{2}$ as $b$ .

Tap for more steps...

Step 4.3.1.2.1

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

$a = x^{2} {(b^{\frac{1}{2}})}^{2}$

Step 4.3.1.2.2

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

$a = x^{2} b^{\frac{1}{2} \cdot 2}$

Step 4.3.1.2.3

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

$a = x^{2} b^{\frac{2}{2}}$

Step 4.3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.3.1.2.4.1

Cancel the common factor.

$a = x^{2} b^{\frac{2}{2}}$

Step 4.3.1.2.4.2

Rewrite the expression.

$a = x^{2} b^{1}$

Step 4.3.1.2.5

Simplify.

$a = x^{2} b$