Solve (zsqrt{5})^4-(2sqrt{3})^3

$$( z \sqrt { 5 } ) ^ { 4 } - ( 2 \sqrt { 3 } ) ^ { 3 }$$

Evaluate

$$25z^{4}-24\sqrt{3}$$

Solution Steps

Expand \left(z\sqrt{5}\right)^{4}.

$$z^{4}\left(\sqrt{5}\right)^{4}-\left(2\sqrt{3}\right)^{3}$$

Expand \left(2\sqrt{3}\right)^{3}.

$$z^{4}\left(\sqrt{5}\right)^{4}-2^{3}\left(\sqrt{3}\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$z^{4}\left(\sqrt{5}\right)^{4}-8\left(\sqrt{3}\right)^{3}$$

Expand

$$25z^{4}-24\sqrt{3}$$

Solution Steps

Expand \left(z\sqrt{5}\right)^{4}.

$$z^{4}\left(\sqrt{5}\right)^{4}-\left(2\sqrt{3}\right)^{3}$$

Expand \left(2\sqrt{3}\right)^{3}.

$$z^{4}\left(\sqrt{5}\right)^{4}-2^{3}\left(\sqrt{3}\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$z^{4}\left(\sqrt{5}\right)^{4}-8\left(\sqrt{3}\right)^{3}$$