Simplify (2 square root of 7+ square root of 14)/( square root of 7)

$\frac{2 \sqrt{7} + \sqrt{14}}{\sqrt{7}}$

Multiply $\frac{2 \sqrt{7} + \sqrt{14}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{2 \sqrt{7} + \sqrt{14}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{7} + \sqrt{14}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{\sqrt{7} \sqrt{7}}$

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

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

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

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

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

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{{\sqrt{7}}^{2}}$

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

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

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

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

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{7^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{7^{1}}$

Evaluate the exponent.

$\frac{(2 \sqrt{7} + \sqrt{14}) \sqrt{7}}{7}$

Apply the distributive property.

$\frac{2 \sqrt{7} \sqrt{7} + \sqrt{14} \sqrt{7}}{7}$

Multiply $2 \sqrt{7} \sqrt{7}$ .

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

$\frac{2 ({\sqrt{7}}^{1} \sqrt{7}) + \sqrt{14} \sqrt{7}}{7}$

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

$\frac{2 ({\sqrt{7}}^{1} {\sqrt{7}}^{1}) + \sqrt{14} \sqrt{7}}{7}$

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

$\frac{2 {\sqrt{7}}^{1 + 1} + \sqrt{14} \sqrt{7}}{7}$

Add $1$ and $1$ .

$\frac{2 {\sqrt{7}}^{2} + \sqrt{14} \sqrt{7}}{7}$

Combine using the product rule for radicals.

$\frac{2 {\sqrt{7}}^{2} + \sqrt{14 \cdot 7}}{7}$

Simplify each term.

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

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

$\frac{2 {(7^{\frac{1}{2}})}^{2} + \sqrt{14 \cdot 7}}{7}$

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

$\frac{2 \cdot 7^{\frac{1}{2} \cdot 2} + \sqrt{14 \cdot 7}}{7}$

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

$\frac{2 \cdot 7^{\frac{2}{2}} + \sqrt{14 \cdot 7}}{7}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 7^{\frac{2}{2}} + \sqrt{14 \cdot 7}}{7}$

Rewrite the expression.

$\frac{2 \cdot 7^{1} + \sqrt{14 \cdot 7}}{7}$

Evaluate the exponent.

$\frac{2 \cdot 7 + \sqrt{14 \cdot 7}}{7}$

Multiply $2$ by $7$ .

$\frac{14 + \sqrt{14 \cdot 7}}{7}$

Multiply $14$ by $7$ .

$\frac{14 + \sqrt{98}}{7}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\frac{14 + \sqrt{49 (2)}}{7}$

Rewrite $49$ as $7^{2}$ .

$\frac{14 + \sqrt{7^{2} \cdot 2}}{7}$

Pull terms out from under the radical.

$\frac{14 + 7 \sqrt{2}}{7}$

Cancel the common factor of $14 + 7 \sqrt{2}$ and $7$ .

Factor $7$ out of $14$ .

$\frac{7 \cdot 2 + 7 \sqrt{2}}{7}$

Factor $7$ out of $7 \sqrt{2}$ .

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

Factor $7$ out of $7 (2) + 7 (\sqrt{2})$ .

$\frac{7 (2 + \sqrt{2})}{7}$

Cancel the common factors.

Factor $7$ out of $7$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 + \sqrt{2}}{1}$

Divide $2 + \sqrt{2}$ by $1$ .

$2 + \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$2 + \sqrt{2}$

Decimal Form:

$3.41421356 \dots$

Simplify (2 square root of 7+ square root of 14)/( square root of 7)

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