Solve sqrt{1}+sqrt{2}+sqrt{3}+sqrt{4}+sqrt{5}+sqrt{6}+sqrt{7}+sqrt{8}+sqrt{9}+sqrt{10}

$$\sqrt{ 1 } + \sqrt{ 2 } + \sqrt{ 3 } + \sqrt{ 4 } + \sqrt{ 5 } + \sqrt{ 6 } + \sqrt{ 7 } + \sqrt{ 8 } + \sqrt{ 9 } + \sqrt{ 10 }$$

Evaluate

$$\sqrt{3}+\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{10}+3\sqrt{2}+6\approx 22.468278186$$

Solution Steps

Calculate the square root of 1 and get 1.

$$1+\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{8}+\sqrt{9}+\sqrt{10}$$

Calculate the square root of 4 and get 2.

$$1+\sqrt{2}+\sqrt{3}+2+\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{8}+\sqrt{9}+\sqrt{10}$$

Add 1 and 2 to get 3.

$$3+\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{8}+\sqrt{9}+\sqrt{10}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$3+\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{6}+\sqrt{7}+2\sqrt{2}+\sqrt{9}+\sqrt{10}$$

Combine \sqrt{2} and 2\sqrt{2} to get 3\sqrt{2}.

$$3+3\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{9}+\sqrt{10}$$

Calculate the square root of 9 and get 3.

$$3+3\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{6}+\sqrt{7}+3+\sqrt{10}$$

Add 3 and 3 to get 6.

$$6+3\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{10}$$