Solve -4sqrt{20}+2sqrt{80}+sqrt{45}quad5

$$- 4 \sqrt { 20 } + 2 \sqrt { 80 } + \sqrt { 45 } \quad 5$$

Evaluate

$$15\sqrt{5}\approx 33.541019662$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$-4\times 2\sqrt{5}+2\sqrt{80}+5\sqrt{45}$$

Multiply -4 and 2 to get -8.

$$-8\sqrt{5}+2\sqrt{80}+5\sqrt{45}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$-8\sqrt{5}+2\times 4\sqrt{5}+5\sqrt{45}$$

Multiply 2 and 4 to get 8.

$$-8\sqrt{5}+8\sqrt{5}+5\sqrt{45}$$

Combine -8\sqrt{5} and 8\sqrt{5} to get 0.

$$5\sqrt{45}$$

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}.

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

Multiply 5 and 3 to get 15.

$$15\sqrt{5}$$