Simplify (2 square root of 8-6)( square root of 8-4)

$(2 \sqrt{8} - 6) (\sqrt{8} - 4)$

Simplify terms.

Simplify each term.

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

Factor $4$ out of $8$ .

$(2 \sqrt{4 (2)} - 6) (\sqrt{8} - 4)$

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

$(2 \sqrt{2^{2} \cdot 2} - 6) (\sqrt{8} - 4)$

Pull terms out from under the radical.

$(2 (2 \sqrt{2}) - 6) (\sqrt{8} - 4)$

Multiply $2$ by $2$ .

$(4 \sqrt{2} - 6) (\sqrt{8} - 4)$

Simplify each term.

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

Factor $4$ out of $8$ .

$(4 \sqrt{2} - 6) (\sqrt{4 (2)} - 4)$

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

$(4 \sqrt{2} - 6) (\sqrt{2^{2} \cdot 2} - 4)$

Pull terms out from under the radical.

$(4 \sqrt{2} - 6) (2 \sqrt{2} - 4)$

Expand $(4 \sqrt{2} - 6) (2 \sqrt{2} - 4)$ using the FOIL Method.

Apply the distributive property.

$4 \sqrt{2} (2 \sqrt{2} - 4) - 6 (2 \sqrt{2} - 4)$

Apply the distributive property.

$4 \sqrt{2} (2 \sqrt{2}) + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2} - 4)$

Apply the distributive property.

$4 \sqrt{2} (2 \sqrt{2}) + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Simplify and combine like terms.

Simplify each term.

Multiply $4 \sqrt{2} (2 \sqrt{2})$ .

Multiply $2$ by $4$ .

$8 \sqrt{2} \sqrt{2} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

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

$8 ({\sqrt{2}}^{1} \sqrt{2}) + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

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

$8 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

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

$8 {\sqrt{2}}^{1 + 1} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Add $1$ and $1$ .

$8 {\sqrt{2}}^{2} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

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

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

$8 {(2^{\frac{1}{2}})}^{2} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

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

$8 \cdot 2^{\frac{1}{2} \cdot 2} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

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

$8 \cdot 2^{\frac{2}{2}} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Cancel the common factor of $2$ .

Cancel the common factor.

$8 \cdot 2^{\frac{2}{2}} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Rewrite the expression.

$8 \cdot 2^{1} + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Evaluate the exponent.

$8 \cdot 2 + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Multiply $8$ by $2$ .

$16 + 4 \sqrt{2} \cdot - 4 - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Multiply $- 4$ by $4$ .

$16 - 16 \sqrt{2} - 6 (2 \sqrt{2}) - 6 \cdot - 4$

Multiply $2$ by $- 6$ .

$16 - 16 \sqrt{2} - 12 \sqrt{2} - 6 \cdot - 4$

Multiply $- 6$ by $- 4$ .

$16 - 16 \sqrt{2} - 12 \sqrt{2} + 24$

Add $16$ and $24$ .

$40 - 16 \sqrt{2} - 12 \sqrt{2}$

Subtract $12 \sqrt{2}$ from $- 16 \sqrt{2}$ .

$40 - 28 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$40 - 28 \sqrt{2}$

Decimal Form:

$0.40202025 \dots$

Simplify (2 square root of 8-6)( square root of 8-4)

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