Solve 4sqrt{10}-2sqrt{90}+6sqrt{250}

$$4 \sqrt { 10 } - 2 \sqrt { 90 } + 6 \sqrt { 250 }$$

Evaluate

$$28\sqrt{10}\approx 88.543774485$$

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}.

$$4\sqrt{10}-2\times 3\sqrt{10}+6\sqrt{250}$$

Multiply -2 and 3 to get -6.

$$4\sqrt{10}-6\sqrt{10}+6\sqrt{250}$$

Combine 4\sqrt{10} and -6\sqrt{10} to get -2\sqrt{10}.

$$-2\sqrt{10}+6\sqrt{250}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

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

Multiply 6 and 5 to get 30.

$$-2\sqrt{10}+30\sqrt{10}$$

Combine -2\sqrt{10} and 30\sqrt{10} to get 28\sqrt{10}.

$$28\sqrt{10}$$