Solve sqrt{54(54-30)(54-48)(54-30)}

$$\sqrt{ 54(54-30)(54-48)(54-30) }$$

Evaluate

$$432$$

Solution Steps

Multiply 54-30 and 54-30 to get \left(54-30\right)^{2}.

$$\sqrt{54\left(54-30\right)^{2}\left(54-48\right)}$$

Subtract 30 from 54 to get 24.

$$\sqrt{54\times 24^{2}\left(54-48\right)}$$

Calculate 24 to the power of 2 and get 576.

$$\sqrt{54\times 576\left(54-48\right)}$$

Multiply 54 and 576 to get 31104.

$$\sqrt{31104\left(54-48\right)}$$

Subtract 48 from 54 to get 6.

$$\sqrt{31104\times 6}$$

Multiply 31104 and 6 to get 186624.

$$\sqrt{186624}$$

Calculate the square root of 186624 and get 432.

$$432$$

Factor

$$2^{4}\times 3^{3}$$