Solve csqrt{32,5^2+12,5^2}

$$c \sqrt { 32,5 ^ { 2 } + 12,5 ^ { 2 } }$$

Evaluate

$$10\sqrt{11}c$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$c\sqrt{32\times 25+12\times 5^{2}}$$

Multiply 32 and 25 to get 800.

$$c\sqrt{800+12\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$c\sqrt{800+12\times 25}$$

Multiply 12 and 25 to get 300.

$$c\sqrt{800+300}$$

Add 800 and 300 to get 1100.

$$c\sqrt{1100}$$

Factor 1100=10^{2}\times 11. Rewrite the square root of the product \sqrt{10^{2}\times 11} as the product of square roots \sqrt{10^{2}}\sqrt{11}. Take the square root of 10^{2}.

$$c\times 10\sqrt{11}$$

Differentiate w.r.t. c

$$10 \sqrt{11} = 33.166247904$$