Solve sqrt{340-28(2)+2^2}-sqrt{2^2+144}

$$\sqrt{ 340-28(2)+ { 2 }^{ 2 } } - \sqrt{ { 2 }^{ 2 } +144 }$$

Evaluate

$$12\sqrt{2}-2\sqrt{37}\approx 4.805037688$$

Solution Steps

Multiply 28 and 2 to get 56.

$$\sqrt{340-56+2^{2}}-\sqrt{2^{2}+144}$$

Subtract 56 from 340 to get 284.

$$\sqrt{284+2^{2}}-\sqrt{2^{2}+144}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{284+4}-\sqrt{2^{2}+144}$$

Add 284 and 4 to get 288.

$$\sqrt{288}-\sqrt{2^{2}+144}$$

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$12\sqrt{2}-\sqrt{2^{2}+144}$$

Calculate 2 to the power of 2 and get 4.

$$12\sqrt{2}-\sqrt{4+144}$$

Add 4 and 144 to get 148.

$$12\sqrt{2}-\sqrt{148}$$

Factor 148=2^{2}\times 37. Rewrite the square root of the product \sqrt{2^{2}\times 37} as the product of square roots \sqrt{2^{2}}\sqrt{37}. Take the square root of 2^{2}.

$$12\sqrt{2}-2\sqrt{37}$$

Factor

$$2 {(6 \sqrt{2} - \sqrt{37})} = 4.805037688$$