Solve 3sqrt{45}-sqrt{80}

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

Evaluate

$$5\sqrt{5}\approx 11.180339887$$

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}.

$$3\times 3\sqrt{5}-\sqrt{80}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{5}-\sqrt{80}$$

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}.

$$9\sqrt{5}-4\sqrt{5}$$

Combine 9\sqrt{5} and -4\sqrt{5} to get 5\sqrt{5}.

$$5\sqrt{5}$$