Solve sqrt{8^2}+sqrt{36}-(sqrt{1}*sqrt{16})+sqrt{8}+8+sqrt{4^2}=

$$\sqrt { 8 ^ { 2 } } + \sqrt { 36 } - ( \sqrt { 1 } \cdot \sqrt { 16 } ) + \sqrt { 8 } + 8 + \sqrt { 4 ^ { 2 } } =$$

Evaluate

$$2\sqrt{2}+22\approx 24.828427125$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt{64}+\sqrt{36}-\sqrt{1}\sqrt{16}+\sqrt{8}+8+\sqrt{4^{2}}$$

Calculate the square root of 64 and get 8.

$$8+\sqrt{36}-\sqrt{1}\sqrt{16}+\sqrt{8}+8+\sqrt{4^{2}}$$

Calculate the square root of 36 and get 6.

$$8+6-\sqrt{1}\sqrt{16}+\sqrt{8}+8+\sqrt{4^{2}}$$

Add 8 and 6 to get 14.

$$14-\sqrt{1}\sqrt{16}+\sqrt{8}+8+\sqrt{4^{2}}$$

Factor 16=1\times 16. Rewrite the square root of the product \sqrt{1\times 16} as the product of square roots \sqrt{1}\sqrt{16}.

$$14-\sqrt{1}\sqrt{1}\sqrt{16}+\sqrt{8}+8+\sqrt{4^{2}}$$

Multiply \sqrt{1} and \sqrt{1} to get 1.

$$14-\sqrt{16}+\sqrt{8}+8+\sqrt{4^{2}}$$

Calculate the square root of 16 and get 4.

$$14-1\times 4+\sqrt{8}+8+\sqrt{4^{2}}$$

Multiply 1 and 4 to get 4.

$$14-4+\sqrt{8}+8+\sqrt{4^{2}}$$

Subtract 4 from 14 to get 10.

$$10+\sqrt{8}+8+\sqrt{4^{2}}$$

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}.

$$10+2\sqrt{2}+8+\sqrt{4^{2}}$$

Add 10 and 8 to get 18.

$$18+2\sqrt{2}+\sqrt{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$18+2\sqrt{2}+\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$18+2\sqrt{2}+4$$

Add 18 and 4 to get 22.

$$22+2\sqrt{2}$$