Solve (5sqrt{3}-sqrt{11})(sqrt{11}+5sqrt{3})

$$( 5 \sqrt { 3 } - \sqrt { 11 } ) ( \sqrt { 11 } + 5 \sqrt { 3 } )$$

Evaluate

$$64$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(5\sqrt{3}\right)^{2}-\left(\sqrt{11}\right)^{2}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$5^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{11}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{3}\right)^{2}-\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{3} is 3.

$$25\times 3-\left(\sqrt{11}\right)^{2}$$

Multiply 25 and 3 to get 75.

$$75-\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$75-11$$

Subtract 11 from 75 to get 64.

$$64$$

Factor

$$2^{6}$$