Solve sqrt{6*40}*sqrt{90}

$$\sqrt{ 6 \times 40 } \times \sqrt{ 90 }$$

Evaluate

$$60\sqrt{6}\approx 146.969384567$$

Solution Steps

Multiply 6 and 40 to get 240.

$$\sqrt{240}\sqrt{90}$$

Factor 240=4^{2}\times 15. Rewrite the square root of the product \sqrt{4^{2}\times 15} as the product of square roots \sqrt{4^{2}}\sqrt{15}. Take the square root of 4^{2}.

$$4\sqrt{15}\sqrt{90}$$

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}.

$$4\sqrt{15}\times 3\sqrt{10}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{15}\sqrt{10}$$

To multiply \sqrt{15} and \sqrt{10}, multiply the numbers under the square root.

$$12\sqrt{150}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$12\times 5\sqrt{6}$$

Multiply 12 and 5 to get 60.

$$60\sqrt{6}$$