Simplify (9- square root of 8)(9+ square root of 8)

$(9 - \sqrt{8}) (9 + \sqrt{8})$

Step 1

Simplify terms.

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$(9 - \sqrt{4 (2)}) (9 + \sqrt{8})$

Rewrite $4$ as $2^{2}$ .

$(9 - \sqrt{2^{2} \cdot 2}) (9 + \sqrt{8})$

Pull terms out from under the radical.

$(9 - (2 \sqrt{2})) (9 + \sqrt{8})$

Multiply $2$ by $- 1$ .

$(9 - 2 \sqrt{2}) (9 + \sqrt{8})$

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$(9 - 2 \sqrt{2}) (9 + \sqrt{4 (2)})$

Rewrite $4$ as $2^{2}$ .

$(9 - 2 \sqrt{2}) (9 + \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$(9 - 2 \sqrt{2}) (9 + 2 \sqrt{2})$

Step 2

Expand $(9 - 2 \sqrt{2}) (9 + 2 \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

$9 (9 + 2 \sqrt{2}) - 2 \sqrt{2} (9 + 2 \sqrt{2})$

Apply the distributive property.

$9 \cdot 9 + 9 (2 \sqrt{2}) - 2 \sqrt{2} (9 + 2 \sqrt{2})$

Apply the distributive property.

$9 \cdot 9 + 9 (2 \sqrt{2}) - 2 \sqrt{2} \cdot 9 - 2 \sqrt{2} (2 \sqrt{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (2 \sqrt{2}) - 2 \sqrt{2} \cdot 9 - 2 \sqrt{2} (2 \sqrt{2})$

Multiply $2$ by $9$ .

$81 + 18 \sqrt{2} - 2 \sqrt{2} \cdot 9 - 2 \sqrt{2} (2 \sqrt{2})$

Multiply $9$ by $- 2$ .

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 2 \sqrt{2} (2 \sqrt{2})$

Multiply $- 2 \sqrt{2} (2 \sqrt{2})$ .

Multiply $2$ by $- 2$ .

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 {\sqrt{2}}^{2}$

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

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

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 {(2^{\frac{1}{2}})}^{2}$

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

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 \cdot 2^{1}$

Evaluate the exponent.

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$81 + 18 \sqrt{2} - 18 \sqrt{2} - 8$

Subtract $8$ from $81$ .

$73 + 18 \sqrt{2} - 18 \sqrt{2}$

Subtract $18 \sqrt{2}$ from $18 \sqrt{2}$ .

$73 + 0$

Add $73$ and $0$ .

$73$

Simplify (9- square root of 8)(9+ square root of 8)

Related Questions

Support LCMGCF.com by disabling your adblocker.