Solve 3sqrt{5}-2sqrt{125}-7sqrt{45}

$$3 \sqrt { 5 } - 2 \sqrt { 125 } - 7 \sqrt { 45 }$$

Evaluate

$$-28\sqrt{5}\approx -62.60990337$$

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}.

$$3\sqrt{5}-2\times 5\sqrt{5}-7\sqrt{45}$$

Multiply -2 and 5 to get -10.

$$3\sqrt{5}-10\sqrt{5}-7\sqrt{45}$$

Combine 3\sqrt{5} and -10\sqrt{5} to get -7\sqrt{5}.

$$-7\sqrt{5}-7\sqrt{45}$$

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}.

$$-7\sqrt{5}-7\times 3\sqrt{5}$$

Multiply -7 and 3 to get -21.

$$-7\sqrt{5}-21\sqrt{5}$$

Combine -7\sqrt{5} and -21\sqrt{5} to get -28\sqrt{5}.

$$-28\sqrt{5}$$