Simplify 4 square root of 22 square root of 8 square root of 20

$4 \sqrt{2} \cdot 2 \sqrt{8} \cdot \sqrt{20}$

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

Factor $4$ out of $8$ .

$4 \sqrt{2} \cdot (2 \sqrt{4 (2)}) \cdot \sqrt{20}$

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

$4 \sqrt{2} \cdot (2 \sqrt{2^{2} \cdot 2}) \cdot \sqrt{20}$

Pull terms out from under the radical.

$4 \sqrt{2} \cdot (2 (2 \sqrt{2})) \cdot \sqrt{20}$

Multiply $2$ by $2$ .

$4 \sqrt{2} \cdot (4 \sqrt{2}) \cdot \sqrt{20}$

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

Multiply $4$ by $4$ .

$16 \sqrt{2} \sqrt{2} \cdot \sqrt{20}$

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

$16 ({\sqrt{2}}^{1} \sqrt{2}) \cdot \sqrt{20}$

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

$16 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) \cdot \sqrt{20}$

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

$16 {\sqrt{2}}^{1 + 1} \cdot \sqrt{20}$

Add $1$ and $1$ .

$16 {\sqrt{2}}^{2} \cdot \sqrt{20}$

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

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

$16 {(2^{\frac{1}{2}})}^{2} \cdot \sqrt{20}$

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

$16 \cdot 2^{\frac{1}{2} \cdot 2} \cdot \sqrt{20}$

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

$16 \cdot 2^{\frac{2}{2}} \cdot \sqrt{20}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 \cdot 2^{\frac{2}{2}} \cdot \sqrt{20}$

Rewrite the expression.

$16 \cdot 2^{1} \cdot \sqrt{20}$

Evaluate the exponent.

$16 \cdot 2 \cdot \sqrt{20}$

Multiply $16$ by $2$ .

$32 \cdot \sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$32 \cdot \sqrt{4 (5)}$

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

$32 \cdot \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$32 \cdot (2 \sqrt{5})$

Multiply $2$ by $32$ .

$64 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$64 \sqrt{5}$

Decimal Form:

$143.10835055 \dots$

Simplify 4 square root of 2*2 square root of 8* square root of 20

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Simplify 4 square root of 22 square root of 8 square root of 20