Solve sqrt{1}+sqrt{1+3}+sqrt{1+3+5}+sqrt{1+3+5+7}=

$$\sqrt{ 1 } + \sqrt{ 1+3 } + \sqrt{ 1+3+5 } + \sqrt{ 1+3+5+7 } =$$

Evaluate

$$10$$

Solution Steps

Calculate the square root of 1 and get 1.

$$1+\sqrt{1+3}+\sqrt{1+3+5}+\sqrt{1+3+5+7}$$

Add 1 and 3 to get 4.

$$1+\sqrt{4}+\sqrt{1+3+5}+\sqrt{1+3+5+7}$$

Calculate the square root of 4 and get 2.

$$1+2+\sqrt{1+3+5}+\sqrt{1+3+5+7}$$

Add 1 and 2 to get 3.

$$3+\sqrt{1+3+5}+\sqrt{1+3+5+7}$$

Add 1 and 3 to get 4.

$$3+\sqrt{4+5}+\sqrt{1+3+5+7}$$

Add 4 and 5 to get 9.

$$3+\sqrt{9}+\sqrt{1+3+5+7}$$

Calculate the square root of 9 and get 3.

$$3+3+\sqrt{1+3+5+7}$$

Add 3 and 3 to get 6.

$$6+\sqrt{1+3+5+7}$$

Add 1 and 3 to get 4.

$$6+\sqrt{4+5+7}$$

Add 4 and 5 to get 9.

$$6+\sqrt{9+7}$$

Add 9 and 7 to get 16.

$$6+\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$6+4$$

Add 6 and 4 to get 10.

$$10$$

Factor

$$2\times 5$$