Solve {left(6sqrt{2}right)}^2-4*27*(-16)

$${ \left(6 \sqrt{ 2 } \right) }^{ 2 } -4 \times 27 \times (-16)$$

Evaluate

$$1800$$

Solution Steps

Expand \left(6\sqrt{2}\right)^{2}.

$$6^{2}\left(\sqrt{2}\right)^{2}-4\times 27\left(-16\right)$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{2}\right)^{2}-4\times 27\left(-16\right)$$

The square of \sqrt{2} is 2.

$$36\times 2-4\times 27\left(-16\right)$$

Multiply 36 and 2 to get 72.

$$72-4\times 27\left(-16\right)$$

Multiply 4 and 27 to get 108.

$$72-108\left(-16\right)$$

Multiply 108 and -16 to get -1728.

$$72-\left(-1728\right)$$

The opposite of -1728 is 1728.

$$72+1728$$

Add 72 and 1728 to get 1800.

$$1800$$

Factor

$$2^{3}\times 3^{2}\times 5^{2}$$