Simplify 4 square root of 310 square root of 12 square root of 6* square root of 2

$4 \sqrt{3} \cdot 10 \sqrt{12} \cdot \sqrt{6} \cdot \sqrt{2}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$4 \sqrt{3} \cdot (10 \sqrt{4 (3)}) \cdot \sqrt{6} \cdot \sqrt{2}$

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

$4 \sqrt{3} \cdot (10 \sqrt{2^{2} \cdot 3}) \cdot \sqrt{6} \cdot \sqrt{2}$

Pull terms out from under the radical.

$4 \sqrt{3} \cdot (10 (2 \sqrt{3})) \cdot \sqrt{6} \cdot \sqrt{2}$

Multiply $2$ by $10$ .

$4 \sqrt{3} \cdot (20 \sqrt{3}) \cdot \sqrt{6} \cdot \sqrt{2}$

Multiply $4 \sqrt{3} (20 \sqrt{3})$ .

Multiply $20$ by $4$ .

$80 \sqrt{3} \sqrt{3} \cdot \sqrt{6} \cdot \sqrt{2}$

Raise $\sqrt{3}$ to the power of $1$ .

$80 ({\sqrt{3}}^{1} \sqrt{3}) \cdot \sqrt{6} \cdot \sqrt{2}$

Raise $\sqrt{3}$ to the power of $1$ .

$80 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) \cdot \sqrt{6} \cdot \sqrt{2}$

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

$80 {\sqrt{3}}^{1 + 1} \cdot \sqrt{6} \cdot \sqrt{2}$

Add $1$ and $1$ .

$80 {\sqrt{3}}^{2} \cdot \sqrt{6} \cdot \sqrt{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$80 {(3^{\frac{1}{2}})}^{2} \cdot \sqrt{6} \cdot \sqrt{2}$

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

$80 \cdot 3^{\frac{1}{2} \cdot 2} \cdot \sqrt{6} \cdot \sqrt{2}$

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

$80 \cdot 3^{\frac{2}{2}} \cdot \sqrt{6} \cdot \sqrt{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$80 \cdot 3^{\frac{2}{2}} \cdot \sqrt{6} \cdot \sqrt{2}$

Rewrite the expression.

$80 \cdot 3^{1} \cdot \sqrt{6} \cdot \sqrt{2}$

Evaluate the exponent.

$80 \cdot 3 \cdot \sqrt{6} \cdot \sqrt{2}$

Multiply $80$ by $3$ .

$240 \cdot \sqrt{6} \cdot \sqrt{2}$

Multiply $240 \sqrt{6} \sqrt{2}$ .

Combine using the product rule for radicals.

$240 \sqrt{2 \cdot 6}$

Multiply $2$ by $6$ .

$240 \sqrt{12}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$240 \sqrt{4 (3)}$

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

$240 \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$240 (2 \sqrt{3})$

Multiply $2$ by $240$ .

$480 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$480 \sqrt{3}$

Decimal Form:

$831.38438763 \dots$

Simplify 4 square root of 3*10 square root of 12* square root of 6* square root of 2

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Simplify 4 square root of 310 square root of 12 square root of 6* square root of 2