Solve 3sqrt{90}-5sqrt{60}+3sqrt{40}+sqrt{100}

$$3 \sqrt { 90 } - 5 \sqrt { 60 } + 3 \sqrt { 40 } + \sqrt { 100 }$$

Evaluate

$$15\sqrt{10}+10-10\sqrt{15}\approx 18.70433144$$

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}.

$$3\times 3\sqrt{10}-5\sqrt{60}+3\sqrt{40}+\sqrt{100}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{10}-5\sqrt{60}+3\sqrt{40}+\sqrt{100}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$9\sqrt{10}-5\times 2\sqrt{15}+3\sqrt{40}+\sqrt{100}$$

Multiply -5 and 2 to get -10.

$$9\sqrt{10}-10\sqrt{15}+3\sqrt{40}+\sqrt{100}$$

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}.

$$9\sqrt{10}-10\sqrt{15}+3\times 2\sqrt{10}+\sqrt{100}$$

Multiply 3 and 2 to get 6.

$$9\sqrt{10}-10\sqrt{15}+6\sqrt{10}+\sqrt{100}$$

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

$$15\sqrt{10}-10\sqrt{15}+\sqrt{100}$$

Calculate the square root of 100 and get 10.

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