Solve frac{(6-3sqrt{5})^2}{(2)^2}

$$\frac { ( 6 - 3 \sqrt { 5 } ) ^ { 2 } } { ( 2 ) ^ { 2 } }$$

Evaluate

$$\frac{81}{4}-9\sqrt{5}\approx 0.125388203$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-3\sqrt{5}\right)^{2}.

$$\frac{36-36\sqrt{5}+9\left(\sqrt{5}\right)^{2}}{2^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{36-36\sqrt{5}+9\times 5}{2^{2}}$$

Multiply 9 and 5 to get 45.

$$\frac{36-36\sqrt{5}+45}{2^{2}}$$

Add 36 and 45 to get 81.

$$\frac{81-36\sqrt{5}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{81-36\sqrt{5}}{4}$$

Expand

$$\frac{81}{4} - 9 \sqrt{5} = 0.125388203$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-3\sqrt{5}\right)^{2}.

$$\frac{36-36\sqrt{5}+9\left(\sqrt{5}\right)^{2}}{2^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{36-36\sqrt{5}+9\times 5}{2^{2}}$$

Multiply 9 and 5 to get 45.

$$\frac{36-36\sqrt{5}+45}{2^{2}}$$

Add 36 and 45 to get 81.

$$\frac{81-36\sqrt{5}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{81-36\sqrt{5}}{4}$$