Solve sqrt{(2+5+3+4/2-2)(2+5+3+4/2-3)(2+5+3+4/2-4)(2+5+3+4/2-5})

$$\sqrt{ ( \frac{ 2+5+3+4 }{ 2 } -2)( \frac{ 2+5+3+4 }{ 2 } -3)( \frac{ 2+5+3+4 }{ 2 } -4)( \frac{ 2+5+3+4 }{ 2 } -5 } )$$

Evaluate

$$2\sqrt{30}\approx 10.95445115$$

Solution Steps

Add 2 and 5 to get 7.

$$\sqrt{\left(\frac{7+3+4}{2}-2\right)\left(\frac{2+5+3+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 7 and 3 to get 10.

$$\sqrt{\left(\frac{10+4}{2}-2\right)\left(\frac{2+5+3+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 10 and 4 to get 14.

$$\sqrt{\left(\frac{14}{2}-2\right)\left(\frac{2+5+3+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Divide 14 by 2 to get 7.

$$\sqrt{\left(7-2\right)\left(\frac{2+5+3+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Subtract 2 from 7 to get 5.

$$\sqrt{5\left(\frac{2+5+3+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 2 and 5 to get 7.

$$\sqrt{5\left(\frac{7+3+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 7 and 3 to get 10.

$$\sqrt{5\left(\frac{10+4}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 10 and 4 to get 14.

$$\sqrt{5\left(\frac{14}{2}-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Divide 14 by 2 to get 7.

$$\sqrt{5\left(7-3\right)\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Subtract 3 from 7 to get 4.

$$\sqrt{5\times 4\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Multiply 5 and 4 to get 20.

$$\sqrt{20\left(\frac{2+5+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 2 and 5 to get 7.

$$\sqrt{20\left(\frac{7+3+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 7 and 3 to get 10.

$$\sqrt{20\left(\frac{10+4}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 10 and 4 to get 14.

$$\sqrt{20\left(\frac{14}{2}-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Divide 14 by 2 to get 7.

$$\sqrt{20\left(7-4\right)\left(\frac{2+5+3+4}{2}-5\right)}$$

Subtract 4 from 7 to get 3.

$$\sqrt{20\times 3\left(\frac{2+5+3+4}{2}-5\right)}$$

Multiply 20 and 3 to get 60.

$$\sqrt{60\left(\frac{2+5+3+4}{2}-5\right)}$$

Add 2 and 5 to get 7.

$$\sqrt{60\left(\frac{7+3+4}{2}-5\right)}$$

Add 7 and 3 to get 10.

$$\sqrt{60\left(\frac{10+4}{2}-5\right)}$$

Add 10 and 4 to get 14.

$$\sqrt{60\left(\frac{14}{2}-5\right)}$$

Divide 14 by 2 to get 7.

$$\sqrt{60\left(7-5\right)}$$

Subtract 5 from 7 to get 2.

$$\sqrt{60\times 2}$$

Multiply 60 and 2 to get 120.

$$\sqrt{120}$$

Factor 120=2^{2}\times 30. Rewrite the square root of the product \sqrt{2^{2}\times 30} as the product of square roots \sqrt{2^{2}}\sqrt{30}. Take the square root of 2^{2}.

$$2\sqrt{30}$$