Solve {left(sqrt{13}-sqrt{11}right)}^2

$${ \left( \sqrt{ 13 } - \sqrt{ 11 } \right) }^{ 2 }$$

Evaluate

$$24-2\sqrt{143}\approx 0.083478514$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{13}-\sqrt{11}\right)^{2}.

$$\left(\sqrt{13}\right)^{2}-2\sqrt{13}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{13} is 13.

$$13-2\sqrt{13}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

To multiply \sqrt{13} and \sqrt{11}, multiply the numbers under the square root.

$$13-2\sqrt{143}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$13-2\sqrt{143}+11$$

Add 13 and 11 to get 24.

$$24-2\sqrt{143}$$

Expand

$$24-2\sqrt{143}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{13}-\sqrt{11}\right)^{2}.

$$\left(\sqrt{13}\right)^{2}-2\sqrt{13}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{13} is 13.

$$13-2\sqrt{13}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

To multiply \sqrt{13} and \sqrt{11}, multiply the numbers under the square root.

$$13-2\sqrt{143}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$13-2\sqrt{143}+11$$

Add 13 and 11 to get 24.

$$24-2\sqrt{143}$$