Solve 2sqrt{15}*sqrt{24}:3sqrt{10}

$$2 \sqrt { 15 } \times \sqrt { 24 } : 3 \sqrt { 10 }$$

Evaluate

$$40$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{15}\times 2\sqrt{6}}{3}\sqrt{10}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{15}\sqrt{6}}{3}\sqrt{10}$$

To multiply \sqrt{15} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{4\sqrt{90}}{3}\sqrt{10}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

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

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{10}}{3}\sqrt{10}$$

Divide 12\sqrt{10} by 3 to get 4\sqrt{10}.

$$4\sqrt{10}\sqrt{10}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$4\times 10$$

Multiply 4 and 10 to get 40.

$$40$$

Factor

$$2^{3}\times 5$$