Solve 3sqrt{250}-4sqrt{90}

$$3 \sqrt { 250 } - 4 \sqrt { 90 }$$

Evaluate

$$3\sqrt{10}\approx 9.486832981$$

Solution Steps

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}.

$$3\times 5\sqrt{10}-4\sqrt{90}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{10}-4\sqrt{90}$$

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}.

$$15\sqrt{10}-4\times 3\sqrt{10}$$

Multiply -4 and 3 to get -12.

$$15\sqrt{10}-12\sqrt{10}$$

Combine 15\sqrt{10} and -12\sqrt{10} to get 3\sqrt{10}.

$$3\sqrt{10}$$