Solve sqrt{5}+6sqrt{125}-4sqrt{5}-2sqrt{45}

$$\sqrt { 5 } + 6 \sqrt { 125 } - 4 \sqrt { 5 } - 2 \sqrt { 45 }$$

Evaluate

$$21\sqrt{5}\approx 46.957427527$$

Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\sqrt{5}+6\times 5\sqrt{5}-4\sqrt{5}-2\sqrt{45}$$

Multiply 6 and 5 to get 30.

$$\sqrt{5}+30\sqrt{5}-4\sqrt{5}-2\sqrt{45}$$

Combine \sqrt{5} and 30\sqrt{5} to get 31\sqrt{5}.

$$31\sqrt{5}-4\sqrt{5}-2\sqrt{45}$$

Combine 31\sqrt{5} and -4\sqrt{5} to get 27\sqrt{5}.

$$27\sqrt{5}-2\sqrt{45}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$27\sqrt{5}-2\times 3\sqrt{5}$$

Multiply -2 and 3 to get -6.

$$27\sqrt{5}-6\sqrt{5}$$

Combine 27\sqrt{5} and -6\sqrt{5} to get 21\sqrt{5}.

$$21\sqrt{5}$$