Simplify ( square root of 7y+1)^2

${(\sqrt{7 y} + 1)}^{2}$

Step 1

Rewrite ${(\sqrt{7 y} + 1)}^{2}$ as $(\sqrt{7 y} + 1) (\sqrt{7 y} + 1)$ .

$(\sqrt{7 y} + 1) (\sqrt{7 y} + 1)$

Step 2

Expand $(\sqrt{7 y} + 1) (\sqrt{7 y} + 1)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{7 y} (\sqrt{7 y} + 1) + 1 (\sqrt{7 y} + 1)$

Apply the distributive property.

$\sqrt{7 y} \sqrt{7 y} + \sqrt{7 y} \cdot 1 + 1 (\sqrt{7 y} + 1)$

Apply the distributive property.

$\sqrt{7 y} \sqrt{7 y} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt{7 y} \sqrt{7 y}$ .

Raise $\sqrt{7 y}$ to the power of $1$ .

${\sqrt{7 y}}^{1} \sqrt{7 y} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Raise $\sqrt{7 y}$ to the power of $1$ .

${\sqrt{7 y}}^{1} {\sqrt{7 y}}^{1} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sqrt{7 y}}^{1 + 1} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Add $1$ and $1$ .

${\sqrt{7 y}}^{2} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Rewrite ${\sqrt{7 y}}^{2}$ as $7 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 y}$ as ${(7 y)}^{\frac{1}{2}}$ .

${({(7 y)}^{\frac{1}{2}})}^{2} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

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

${(7 y)}^{\frac{1}{2} \cdot 2} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

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

${(7 y)}^{\frac{2}{2}} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 y)}^{\frac{2}{2}} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Rewrite the expression.

${(7 y)}^{1} + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Simplify.

$7 y + \sqrt{7 y} \cdot 1 + 1 \sqrt{7 y} + 1 \cdot 1$

Multiply $\sqrt{7 y}$ by $1$ .

$7 y + \sqrt{7 y} + 1 \sqrt{7 y} + 1 \cdot 1$

Multiply $\sqrt{7 y}$ by $1$ .

$7 y + \sqrt{7 y} + \sqrt{7 y} + 1 \cdot 1$

Multiply $1$ by $1$ .

$7 y + \sqrt{7 y} + \sqrt{7 y} + 1$

Add $\sqrt{7 y}$ and $\sqrt{7 y}$ .

$7 y + 2 \sqrt{7 y} + 1$

Simplify ( square root of 7y+1)^2

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