Solve sqrt{45}+3sqrt{2}-sqrt{80}

$$\sqrt{ 45 } +3 \sqrt{ 2 } - \sqrt{ 80 }$$

Evaluate

$$3\sqrt{2}-\sqrt{5}\approx 2.00657271$$

Solution Steps

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}.

$$3\sqrt{5}+3\sqrt{2}-\sqrt{80}$$

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}.

$$3\sqrt{5}+3\sqrt{2}-4\sqrt{5}$$

Combine 3\sqrt{5} and -4\sqrt{5} to get -\sqrt{5}.

$$-\sqrt{5}+3\sqrt{2}$$