Solve 2sqrt{45}-2sqrt{20}

$$2 \sqrt { 45 } - 2 \sqrt { 20 }$$

Evaluate

$$2\sqrt{5}\approx 4.472135955$$

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}.

$$2\times 3\sqrt{5}-2\sqrt{20}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{5}-2\sqrt{20}$$

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}.

$$6\sqrt{5}-2\times 2\sqrt{5}$$

Multiply -2 and 2 to get -4.

$$6\sqrt{5}-4\sqrt{5}$$

Combine 6\sqrt{5} and -4\sqrt{5} to get 2\sqrt{5}.

$$2\sqrt{5}$$