Solve 15sqrt{30*20}*sqrt{60}

$$15 \sqrt { 30 \cdot 20 } \cdot \sqrt { 60 }$$

Evaluate

$$900\sqrt{10}\approx 2846.049894152$$

Solution Steps

Multiply 30 and 20 to get 600.

$$15\sqrt{600}\sqrt{60}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$15\times 10\sqrt{6}\sqrt{60}$$

Multiply 15 and 10 to get 150.

$$150\sqrt{6}\sqrt{60}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$150\sqrt{6}\times 2\sqrt{15}$$

Multiply 150 and 2 to get 300.

$$300\sqrt{6}\sqrt{15}$$

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

$$300\sqrt{90}$$

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}.

$$300\times 3\sqrt{10}$$

Multiply 300 and 3 to get 900.

$$900\sqrt{10}$$