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

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

Evaluate

$$60\sqrt{3}\approx 103.923048454$$

Solution Steps

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$3\times 5\sqrt{2}\sqrt{2}\sqrt{12}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$3\times 5\times 2\sqrt{12}$$

Multiply 3 and 5 to get 15.

$$15\times 2\sqrt{12}$$

Multiply 15 and 2 to get 30.

$$30\sqrt{12}$$

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}.

$$30\times 2\sqrt{3}$$

Multiply 30 and 2 to get 60.

$$60\sqrt{3}$$