Basic Math Examples

$\sqrt{6 y + 2} = \sqrt{5 y + 5}$

Step 1

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

${\sqrt{6 y + 2}}^{2} = {\sqrt{5 y + 5}}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

${({(6 y + 2)}^{\frac{1}{2}})}^{2} = {\sqrt{5 y + 5}}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(6 y + 2)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(6 y + 2)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(6 y + 2)}^{\frac{1}{2} \cdot 2} = {\sqrt{5 y + 5}}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(6 y + 2)}^{\frac{1}{2} \cdot 2} = {\sqrt{5 y + 5}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(6 y + 2)}^{1} = {\sqrt{5 y + 5}}^{2}$

Step 2.2.1.2

Simplify.

$6 y + 2 = {\sqrt{5 y + 5}}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify ${\sqrt{5 y + 5}}^{2}$ .

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Step 2.3.1.1

Factor $5$ out of $5 y + 5$ .

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Step 2.3.1.1.1

Factor $5$ out of $5 y$ .

$6 y + 2 = {\sqrt{5 (y) + 5}}^{2}$

Step 2.3.1.1.2

Factor $5$ out of $5$ .

$6 y + 2 = {\sqrt{5 (y) + 5 (1)}}^{2}$

Step 2.3.1.1.3

Factor $5$ out of $5 (y) + 5 (1)$ .

$6 y + 2 = {\sqrt{5 (y + 1)}}^{2}$

Step 2.3.1.2

Rewrite ${\sqrt{5 (y + 1)}}^{2}$ as $5 (y + 1)$ .

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Step 2.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 (y + 1)}$ as ${(5 (y + 1))}^{\frac{1}{2}}$ .

$6 y + 2 = {({(5 (y + 1))}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2.2

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

$6 y + 2 = {(5 (y + 1))}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.2.3

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

$6 y + 2 = {(5 (y + 1))}^{\frac{2}{2}}$

Step 2.3.1.2.4

Cancel the common factor of $2$ .

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Step 2.3.1.2.4.1

Cancel the common factor.

$6 y + 2 = {(5 (y + 1))}^{\frac{2}{2}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$6 y + 2 = {(5 (y + 1))}^{1}$

Step 2.3.1.2.5

Simplify.

$6 y + 2 = 5 (y + 1)$

Step 2.3.1.3

Apply the distributive property.

$6 y + 2 = 5 y + 5 \cdot 1$

Step 2.3.1.4

Multiply $5$ by $1$ .

$6 y + 2 = 5 y + 5$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5 y$ from both sides of the equation.

$6 y + 2 - 5 y = 5$

Step 3.1.2

Subtract $5 y$ from $6 y$ .

$y + 2 = 5$

Step 3.2

Move all terms not containing $y$ to the right side of the equation.

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Step 3.2.1

Subtract $2$ from both sides of the equation.

$y = 5 - 2$

Step 3.2.2

Subtract $2$ from $5$ .

$y = 3$