Solve 4sqrt{45}+3sqrt{20}

$$4 \sqrt { 45 } + 3 \sqrt { 20 }$$

Evaluate

$$18\sqrt{5}\approx 40.249223595$$

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}.

$$4\times 3\sqrt{5}+3\sqrt{20}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{5}+3\sqrt{20}$$

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}.

$$12\sqrt{5}+3\times 2\sqrt{5}$$

Multiply 3 and 2 to get 6.

$$12\sqrt{5}+6\sqrt{5}$$

Combine 12\sqrt{5} and 6\sqrt{5} to get 18\sqrt{5}.

$$18\sqrt{5}$$