Solve 3sqrt{20}+8sqrt{45}

$$3 \sqrt{ 20 } +8 \sqrt{ 45 }$$

Evaluate

$$30\sqrt{5}\approx 67.082039325$$

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}.

$$3\times 2\sqrt{5}+8\sqrt{45}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{5}+8\sqrt{45}$$

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}.

$$6\sqrt{5}+8\times 3\sqrt{5}$$

Multiply 8 and 3 to get 24.

$$6\sqrt{5}+24\sqrt{5}$$

Combine 6\sqrt{5} and 24\sqrt{5} to get 30\sqrt{5}.

$$30\sqrt{5}$$