Solve 6sqrt{147}+3sqrt{75}-2sqrt{40}=

$$6 \sqrt { 147 } + 3 \sqrt { 75 } - 2 \sqrt { 40 } =$$

Evaluate

$$57\sqrt{3}-4\sqrt{10}\approx 86.077785391$$

Solution Steps

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$6\times 7\sqrt{3}+3\sqrt{75}-2\sqrt{40}$$

Multiply 6 and 7 to get 42.

$$42\sqrt{3}+3\sqrt{75}-2\sqrt{40}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$42\sqrt{3}+3\times 5\sqrt{3}-2\sqrt{40}$$

Multiply 3 and 5 to get 15.

$$42\sqrt{3}+15\sqrt{3}-2\sqrt{40}$$

Combine 42\sqrt{3} and 15\sqrt{3} to get 57\sqrt{3}.

$$57\sqrt{3}-2\sqrt{40}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$57\sqrt{3}-2\times 2\sqrt{10}$$

Multiply -2 and 2 to get -4.

$$57\sqrt{3}-4\sqrt{10}$$