Solve (10sqrt{48}+4sqrt{12})div3

$$(10 \sqrt{ 48 } +4 \sqrt{ 12 } ) \div 3$$

Evaluate

$$16\sqrt{3}\approx 27.712812921$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{10\times 4\sqrt{3}+4\sqrt{12}}{3}$$

Multiply 10 and 4 to get 40.

$$\frac{40\sqrt{3}+4\sqrt{12}}{3}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{40\sqrt{3}+4\times 2\sqrt{3}}{3}$$

Multiply 4 and 2 to get 8.

$$\frac{40\sqrt{3}+8\sqrt{3}}{3}$$

Combine 40\sqrt{3} and 8\sqrt{3} to get 48\sqrt{3}.

$$\frac{48\sqrt{3}}{3}$$

Divide 48\sqrt{3} by 3 to get 16\sqrt{3}.

$$16\sqrt{3}$$