Solve 5sqrt{3}*2sqrt{24}

$$5 \sqrt { 3 } \cdot 2 \sqrt { 24 }$$

Evaluate

$$60\sqrt{2}\approx 84.852813742$$

Solution Steps

Factor 24=3\times 8. Rewrite the square root of the product \sqrt{3\times 8} as the product of square roots \sqrt{3}\sqrt{8}.

$$2\times 5\sqrt{3}\sqrt{3}\sqrt{8}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 5\times 3\sqrt{8}$$

Multiply 2 and 5 to get 10.

$$10\times 3\sqrt{8}$$

Multiply 10 and 3 to get 30.

$$30\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$30\times 2\sqrt{2}$$

Multiply 30 and 2 to get 60.

$$60\sqrt{2}$$