Solve sqrt{75(75-30)(75-72)(75-78)}

$$\sqrt { 75 ( 75 - 30 ) ( 75 - 72 ) ( 75 - 78 ) }$$

Evaluate (complex solution)

$$45\sqrt{15}i\approx 174.284250579i$$

Solution Steps

Subtract 30 from 75 to get 45.

$$\sqrt{75\times 45\left(75-72\right)\left(75-78\right)}$$

Multiply 75 and 45 to get 3375.

$$\sqrt{3375\left(75-72\right)\left(75-78\right)}$$

Subtract 72 from 75 to get 3.

$$\sqrt{3375\times 3\left(75-78\right)}$$

Multiply 3375 and 3 to get 10125.

$$\sqrt{10125\left(75-78\right)}$$

Subtract 78 from 75 to get -3.

$$\sqrt{10125\left(-3\right)}$$

Multiply 10125 and -3 to get -30375.

$$\sqrt{-30375}$$

Factor -30375=\left(45i\right)^{2}\times 15. Rewrite the square root of the product \sqrt{\left(45i\right)^{2}\times 15} as the product of square roots \sqrt{\left(45i\right)^{2}}\sqrt{15}. Take the square root of \left(45i\right)^{2}.

$$45i\sqrt{15}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$