Solve sqrt{(30)(30}-12)(30-12)(30-15)

$$\sqrt{ (30)(30 } -12)(30-12)(30-15)$$

Evaluate

$$540\sqrt{222}\approx 8045.818789906$$

Solution Steps

Multiply 30 and 30 to get 900.

$$\sqrt{900-12}\left(30-12\right)\left(30-15\right)$$

Subtract 12 from 900 to get 888.

$$\sqrt{888}\left(30-12\right)\left(30-15\right)$$

Factor 888=2^{2}\times 222. Rewrite the square root of the product \sqrt{2^{2}\times 222} as the product of square roots \sqrt{2^{2}}\sqrt{222}. Take the square root of 2^{2}.

$$2\sqrt{222}\left(30-12\right)\left(30-15\right)$$

Subtract 12 from 30 to get 18.

$$2\sqrt{222}\times 18\left(30-15\right)$$

Multiply 2 and 18 to get 36.

$$36\sqrt{222}\left(30-15\right)$$

Subtract 15 from 30 to get 15.

$$36\sqrt{222}\times 15$$

Multiply 36 and 15 to get 540.

$$540\sqrt{222}$$