Solve sqrt{3*45}sqrt{8}

$$\sqrt{ 3 \cdot 45 } \sqrt{ 8 }$$

Evaluate

$$6\sqrt{30}\approx 32.86335345$$

Solution Steps

Multiply 3 and 45 to get 135.

$$\sqrt{135}\sqrt{8}$$

Factor 135=3^{2}\times 15. Rewrite the square root of the product \sqrt{3^{2}\times 15} as the product of square roots \sqrt{3^{2}}\sqrt{15}. Take the square root of 3^{2}.

$$3\sqrt{15}\sqrt{8}$$

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}.

$$3\sqrt{15}\times 2\sqrt{2}$$

Multiply 3 and 2 to get 6.

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

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$6\sqrt{30}$$