Basic Math Examples

$v ({(- \sqrt{5} - 6 \sqrt{5})}^{2} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1

Simplify each term.

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Step 1.1

Subtract $6 \sqrt{5}$ from $- \sqrt{5}$ .

$v ({(- 7 \sqrt{5})}^{2} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.2

Apply the product rule to $- 7 \sqrt{5}$ .

$v ({(- 7)}^{2} {\sqrt{5}}^{2} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.3

Raise $- 7$ to the power of $2$ .

$v (49 {\sqrt{5}}^{2} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.4

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 1.4.1

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

$v (49 {(5^{\frac{1}{2}})}^{2} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.4.2

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

$v (49 \cdot 5^{\frac{1}{2} \cdot 2} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.4.3

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

$v (49 \cdot 5^{\frac{2}{2}} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.4.4

Cancel the common factor of $2$ .

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Step 1.4.4.1

Cancel the common factor.

$v (49 \cdot 5^{\frac{2}{2}} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.4.4.2

Rewrite the expression.

$v (49 \cdot 5^{1} + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.4.5

Evaluate the exponent.

$v (49 \cdot 5 + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.5

Multiply $49$ by $5$ .

$v (245 + {(2 \sqrt{6} - \sqrt{6})}^{2})$

Step 1.6

Subtract $\sqrt{6}$ from $2 \sqrt{6}$ .

$v (245 + {\sqrt{6}}^{2})$

Step 1.7

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

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Step 1.7.1

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

$v (245 + {(6^{\frac{1}{2}})}^{2})$

Step 1.7.2

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

$v (245 + 6^{\frac{1}{2} \cdot 2})$

Step 1.7.3

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

$v (245 + 6^{\frac{2}{2}})$

Step 1.7.4

Cancel the common factor of $2$ .

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Step 1.7.4.1

Cancel the common factor.

$v (245 + 6^{\frac{2}{2}})$

Step 1.7.4.2

Rewrite the expression.

$v (245 + 6^{1})$

Step 1.7.5

Evaluate the exponent.

$v (245 + 6)$

Step 2

Simplify the expression.

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Step 2.1

Add $245$ and $6$ .

$v \cdot 251$

Step 2.2

Move $251$ to the left of $v$ .

$251 v$