Solve 6sqrt{10}-5sqrt{90}-3sqrt{10}+4sqrt{40}

$$6 \sqrt { 10 } - 5 \sqrt { 90 } - 3 \sqrt { 10 } + 4 \sqrt { 40 }$$

Evaluate

$$-4\sqrt{10}\approx -12.649110641$$

Solution Steps

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}.

$$6\sqrt{10}-5\times 3\sqrt{10}-3\sqrt{10}+4\sqrt{40}$$

Multiply -5 and 3 to get -15.

$$6\sqrt{10}-15\sqrt{10}-3\sqrt{10}+4\sqrt{40}$$

Combine 6\sqrt{10} and -15\sqrt{10} to get -9\sqrt{10}.

$$-9\sqrt{10}-3\sqrt{10}+4\sqrt{40}$$

Combine -9\sqrt{10} and -3\sqrt{10} to get -12\sqrt{10}.

$$-12\sqrt{10}+4\sqrt{40}$$

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}.

$$-12\sqrt{10}+4\times 2\sqrt{10}$$

Multiply 4 and 2 to get 8.

$$-12\sqrt{10}+8\sqrt{10}$$

Combine -12\sqrt{10} and 8\sqrt{10} to get -4\sqrt{10}.

$$-4\sqrt{10}$$