Solve {left(15-5sqrt{3}right)}^2-5sqrt{3}

$${ \left(15-5 \sqrt{ 3 } \right) }^{ 2 } -5 \sqrt{ 3 }$$

Evaluate

$$300-155\sqrt{3}\approx 31.532124827$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15-5\sqrt{3}\right)^{2}.

$$225-150\sqrt{3}+25\left(\sqrt{3}\right)^{2}-5\sqrt{3}$$

The square of \sqrt{3} is 3.

$$225-150\sqrt{3}+25\times 3-5\sqrt{3}$$

Multiply 25 and 3 to get 75.

$$225-150\sqrt{3}+75-5\sqrt{3}$$

Add 225 and 75 to get 300.

$$300-150\sqrt{3}-5\sqrt{3}$$

Combine -150\sqrt{3} and -5\sqrt{3} to get -155\sqrt{3}.

$$300-155\sqrt{3}$$

Factor

$$5 {(60 - 31 \sqrt{3})} = 31.532124827$$