Simplify (6+ square root of 23)(6- square root of 23)

$(6 + \sqrt{23}) (6 - \sqrt{23})$

Step 1

Expand $(6 + \sqrt{23}) (6 - \sqrt{23})$ using the FOIL Method.

Apply the distributive property.

$6 (6 - \sqrt{23}) + \sqrt{23} (6 - \sqrt{23})$

Apply the distributive property.

$6 \cdot 6 + 6 (- \sqrt{23}) + \sqrt{23} (6 - \sqrt{23})$

Apply the distributive property.

$6 \cdot 6 + 6 (- \sqrt{23}) + \sqrt{23} \cdot 6 + \sqrt{23} (- \sqrt{23})$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 (- \sqrt{23}) + \sqrt{23} \cdot 6 + \sqrt{23} (- \sqrt{23})$

Multiply $- 1$ by $6$ .

$36 - 6 \sqrt{23} + \sqrt{23} \cdot 6 + \sqrt{23} (- \sqrt{23})$

Move $6$ to the left of $\sqrt{23}$ .

$36 - 6 \sqrt{23} + 6 \cdot \sqrt{23} + \sqrt{23} (- \sqrt{23})$

Multiply $\sqrt{23} (- \sqrt{23})$ .

Raise $\sqrt{23}$ to the power of $1$ .

$36 - 6 \sqrt{23} + 6 \sqrt{23} - ({\sqrt{23}}^{1} \sqrt{23})$

Raise $\sqrt{23}$ to the power of $1$ .

$36 - 6 \sqrt{23} + 6 \sqrt{23} - ({\sqrt{23}}^{1} {\sqrt{23}}^{1})$

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

$36 - 6 \sqrt{23} + 6 \sqrt{23} - {\sqrt{23}}^{1 + 1}$

Add $1$ and $1$ .

$36 - 6 \sqrt{23} + 6 \sqrt{23} - {\sqrt{23}}^{2}$

Rewrite ${\sqrt{23}}^{2}$ as $23$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{23}$ as $23^{\frac{1}{2}}$ .

$36 - 6 \sqrt{23} + 6 \sqrt{23} - {(23^{\frac{1}{2}})}^{2}$

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

$36 - 6 \sqrt{23} + 6 \sqrt{23} - 23^{\frac{1}{2} \cdot 2}$

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

$36 - 6 \sqrt{23} + 6 \sqrt{23} - 23^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$36 - 6 \sqrt{23} + 6 \sqrt{23} - 23^{\frac{2}{2}}$

Rewrite the expression.

$36 - 6 \sqrt{23} + 6 \sqrt{23} - 23^{1}$

Evaluate the exponent.

$36 - 6 \sqrt{23} + 6 \sqrt{23} - 1 \cdot 23$

Multiply $- 1$ by $23$ .

$36 - 6 \sqrt{23} + 6 \sqrt{23} - 23$

Subtract $23$ from $36$ .

$13 - 6 \sqrt{23} + 6 \sqrt{23}$

Add $- 6 \sqrt{23}$ and $6 \sqrt{23}$ .

$13 + 0$

Add $13$ and $0$ .

$13$

Simplify (6+ square root of 23)(6- square root of 23)

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