Solve {left(sqrt{7}+sqrt{11}right)}^2

$${ \left( \sqrt{ 7 } + \sqrt{ 11 } \right) }^{ 2 }$$

Evaluate

$$2\left(\sqrt{77}+9\right)\approx 35.549928775$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{7}+\sqrt{11}\right)^{2}.

$$\left(\sqrt{7}\right)^{2}+2\sqrt{7}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7+2\sqrt{7}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

To multiply \sqrt{7} and \sqrt{11}, multiply the numbers under the square root.

$$7+2\sqrt{77}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$7+2\sqrt{77}+11$$

Add 7 and 11 to get 18.

$$18+2\sqrt{77}$$

Expand

$$2 \sqrt{77} + 18 = 35.549928775$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{7}+\sqrt{11}\right)^{2}.

$$\left(\sqrt{7}\right)^{2}+2\sqrt{7}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7+2\sqrt{7}\sqrt{11}+\left(\sqrt{11}\right)^{2}$$

To multiply \sqrt{7} and \sqrt{11}, multiply the numbers under the square root.

$$7+2\sqrt{77}+\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$7+2\sqrt{77}+11$$

Add 7 and 11 to get 18.

$$18+2\sqrt{77}$$