Solve 3sqrt{40}+sqrt{250}+3sqrt{360}-4sqrt{810}

$$3 \sqrt{ 40 } + \sqrt{ 250 } +3 \sqrt{ 360 } -4 \sqrt{ 810 }$$

Evaluate

$$-7\sqrt{10}\approx -22.135943621$$

Solution Steps

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}.

$$3\times 2\sqrt{10}+\sqrt{250}+3\sqrt{360}-4\sqrt{810}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{10}+\sqrt{250}+3\sqrt{360}-4\sqrt{810}$$

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}.

$$6\sqrt{10}+5\sqrt{10}+3\sqrt{360}-4\sqrt{810}$$

Combine 6\sqrt{10} and 5\sqrt{10} to get 11\sqrt{10}.

$$11\sqrt{10}+3\sqrt{360}-4\sqrt{810}$$

Factor 360=6^{2}\times 10. Rewrite the square root of the product \sqrt{6^{2}\times 10} as the product of square roots \sqrt{6^{2}}\sqrt{10}. Take the square root of 6^{2}.

$$11\sqrt{10}+3\times 6\sqrt{10}-4\sqrt{810}$$

Multiply 3 and 6 to get 18.

$$11\sqrt{10}+18\sqrt{10}-4\sqrt{810}$$

Combine 11\sqrt{10} and 18\sqrt{10} to get 29\sqrt{10}.

$$29\sqrt{10}-4\sqrt{810}$$

Factor 810=9^{2}\times 10. Rewrite the square root of the product \sqrt{9^{2}\times 10} as the product of square roots \sqrt{9^{2}}\sqrt{10}. Take the square root of 9^{2}.

$$29\sqrt{10}-4\times 9\sqrt{10}$$

Multiply -4 and 9 to get -36.

$$29\sqrt{10}-36\sqrt{10}$$

Combine 29\sqrt{10} and -36\sqrt{10} to get -7\sqrt{10}.

$$-7\sqrt{10}$$