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

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

Evaluate

$$-2\sqrt{22}\approx -9.38083152$$

Solution Steps

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

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

The square of \sqrt{11} is 11.

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

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$11-2\sqrt{22}+\left(\sqrt{2}\right)^{2}-13$$

The square of \sqrt{2} is 2.

$$11-2\sqrt{22}+2-13$$

Add 11 and 2 to get 13.

$$13-2\sqrt{22}-13$$

Subtract 13 from 13 to get 0.

$$-2\sqrt{22}$$

Expand

$$-2\sqrt{22}$$

Solution Steps

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

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

The square of \sqrt{11} is 11.

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

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$11-2\sqrt{22}+\left(\sqrt{2}\right)^{2}-13$$

The square of \sqrt{2} is 2.

$$11-2\sqrt{22}+2-13$$

Add 11 and 2 to get 13.

$$13-2\sqrt{22}-13$$

Subtract 13 from 13 to get 0.

$$-2\sqrt{22}$$