Basic Math Examples

$\sqrt{y} - \sqrt{6} = 5 \sqrt{6}$

Step 1

Move all terms not containing $\sqrt{y}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $\sqrt{6}$ to both sides of the equation.

$\sqrt{y} = 5 \sqrt{6} + \sqrt{6}$

Step 1.2

Add $5 \sqrt{6}$ and $\sqrt{6}$ .

$\sqrt{y} = 6 \sqrt{6}$

Step 2

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

${\sqrt{y}}^{2} = {(6 \sqrt{6})}^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

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

${(y^{\frac{1}{2}})}^{2} = {(6 \sqrt{6})}^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

Tap for more steps...

Step 3.2.1.1.1

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

$y^{\frac{1}{2} \cdot 2} = {(6 \sqrt{6})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = {(6 \sqrt{6})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$y^{1} = {(6 \sqrt{6})}^{2}$

Step 3.2.1.2

Simplify.

$y = {(6 \sqrt{6})}^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify ${(6 \sqrt{6})}^{2}$ .

Tap for more steps...

Step 3.3.1.1

Simplify the expression.

Tap for more steps...

Step 3.3.1.1.1

Apply the product rule to $6 \sqrt{6}$ .

$y = 6^{2} {\sqrt{6}}^{2}$

Step 3.3.1.1.2

Raise $6$ to the power of $2$ .

$y = 36 {\sqrt{6}}^{2}$

Step 3.3.1.2

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Tap for more steps...

Step 3.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$y = 36 {(6^{\frac{1}{2}})}^{2}$

Step 3.3.1.2.2

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

$y = 36 \cdot 6^{\frac{1}{2} \cdot 2}$

Step 3.3.1.2.3

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

$y = 36 \cdot 6^{\frac{2}{2}}$

Step 3.3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.1.2.4.1

Cancel the common factor.

$y = 36 \cdot 6^{\frac{2}{2}}$

Step 3.3.1.2.4.2

Rewrite the expression.

$y = 36 \cdot 6^{1}$

Step 3.3.1.2.5

Evaluate the exponent.

$y = 36 \cdot 6$

Step 3.3.1.3

Multiply $36$ by $6$ .

$y = 216$