Solve sqrt{12^2+12^2+2*12*12*0.5}

$$\sqrt{ { 12 }^{ 2 } + { 12 }^{ 2 } +2 \cdot 12 \cdot 12 \cdot 0.5 }$$

Evaluate

$$12\sqrt{3}\approx 20.784609691$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144+12^{2}+2\times 12\times 12\times 0.5}$$

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144+144+2\times 12\times 12\times 0.5}$$

Add 144 and 144 to get 288.

$$\sqrt{288+2\times 12\times 12\times 0.5}$$

Multiply 2 and 12 to get 24.

$$\sqrt{288+24\times 12\times 0.5}$$

Multiply 24 and 12 to get 288.

$$\sqrt{288+288\times 0.5}$$

Multiply 288 and 0.5 to get 144.

$$\sqrt{288+144}$$

Add 288 and 144 to get 432.

$$\sqrt{432}$$

Factor 432=12^{2}\times 3. Rewrite the square root of the product \sqrt{12^{2}\times 3} as the product of square roots \sqrt{12^{2}}\sqrt{3}. Take the square root of 12^{2}.

$$12\sqrt{3}$$