Solve =2sqrt{90}-5sqrt{40}

$$= 2 \sqrt { 90 } - 5 \sqrt { 40 }$$

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}.

$$2\times 3\sqrt{10}-5\sqrt{40}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{10}-5\sqrt{40}$$

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}.

$$6\sqrt{10}-5\times 2\sqrt{10}$$

Multiply -5 and 2 to get -10.

$$6\sqrt{10}-10\sqrt{10}$$

Combine 6\sqrt{10} and -10\sqrt{10} to get -4\sqrt{10}.

$$-4\sqrt{10}$$