Solve sqrt{8^2+36+0}+sqrt{1+16+64}+sqrt{81+100+64}

$$\sqrt{ { 8 }^{ 2 } +36+0 } + \sqrt{ 1+16+64 } + \sqrt{ 81+100+64 }$$

Evaluate

$$7\sqrt{5}+19\approx 34.652475842$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt{64+36+0}+\sqrt{1+16+64}+\sqrt{81+100+64}$$

Add 64 and 36 to get 100.

$$\sqrt{100+0}+\sqrt{1+16+64}+\sqrt{81+100+64}$$

Add 100 and 0 to get 100.

$$\sqrt{100}+\sqrt{1+16+64}+\sqrt{81+100+64}$$

Calculate the square root of 100 and get 10.

$$10+\sqrt{1+16+64}+\sqrt{81+100+64}$$

Add 1 and 16 to get 17.

$$10+\sqrt{17+64}+\sqrt{81+100+64}$$

Add 17 and 64 to get 81.

$$10+\sqrt{81}+\sqrt{81+100+64}$$

Calculate the square root of 81 and get 9.

$$10+9+\sqrt{81+100+64}$$

Add 10 and 9 to get 19.

$$19+\sqrt{81+100+64}$$

Add 81 and 100 to get 181.

$$19+\sqrt{181+64}$$

Add 181 and 64 to get 245.

$$19+\sqrt{245}$$

Factor 245=7^{2}\times 5. Rewrite the square root of the product \sqrt{7^{2}\times 5} as the product of square roots \sqrt{7^{2}}\sqrt{5}. Take the square root of 7^{2}.

$$19+7\sqrt{5}$$