Simplify (6- square root of 11)(6+ square root of 11)

$(6 - \sqrt{11}) (6 + \sqrt{11})$

Step 1

Expand $(6 - \sqrt{11}) (6 + \sqrt{11})$ using the FOIL Method.

Apply the distributive property.

$6 (6 + \sqrt{11}) - \sqrt{11} (6 + \sqrt{11})$

Apply the distributive property.

$6 \cdot 6 + 6 \sqrt{11} - \sqrt{11} (6 + \sqrt{11})$

Apply the distributive property.

$6 \cdot 6 + 6 \sqrt{11} - \sqrt{11} \cdot 6 - \sqrt{11} \sqrt{11}$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 \sqrt{11} - \sqrt{11} \cdot 6 - \sqrt{11} \sqrt{11}$

Multiply $6$ by $- 1$ .

$36 + 6 \sqrt{11} - 6 \sqrt{11} - \sqrt{11} \sqrt{11}$

Multiply $- \sqrt{11} \sqrt{11}$ .

Raise $\sqrt{11}$ to the power of $1$ .

$36 + 6 \sqrt{11} - 6 \sqrt{11} - ({\sqrt{11}}^{1} \sqrt{11})$

Raise $\sqrt{11}$ to the power of $1$ .

$36 + 6 \sqrt{11} - 6 \sqrt{11} - ({\sqrt{11}}^{1} {\sqrt{11}}^{1})$

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

$36 + 6 \sqrt{11} - 6 \sqrt{11} - {\sqrt{11}}^{1 + 1}$

Add $1$ and $1$ .

$36 + 6 \sqrt{11} - 6 \sqrt{11} - {\sqrt{11}}^{2}$

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$36 + 6 \sqrt{11} - 6 \sqrt{11} - {(11^{\frac{1}{2}})}^{2}$

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

$36 + 6 \sqrt{11} - 6 \sqrt{11} - 11^{\frac{1}{2} \cdot 2}$

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

$36 + 6 \sqrt{11} - 6 \sqrt{11} - 11^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$36 + 6 \sqrt{11} - 6 \sqrt{11} - 11^{\frac{2}{2}}$

Rewrite the expression.

$36 + 6 \sqrt{11} - 6 \sqrt{11} - 11^{1}$

Evaluate the exponent.

$36 + 6 \sqrt{11} - 6 \sqrt{11} - 1 \cdot 11$

Multiply $- 1$ by $11$ .

$36 + 6 \sqrt{11} - 6 \sqrt{11} - 11$

Subtract $11$ from $36$ .

$25 + 6 \sqrt{11} - 6 \sqrt{11}$

Subtract $6 \sqrt{11}$ from $6 \sqrt{11}$ .

$25 + 0$

Add $25$ and $0$ .

$25$

Simplify (6- square root of 11)(6+ square root of 11)

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