Question

The value of $(\sqrt{7}+\sqrt{3}{)}^2$ is:

• A. $0$
• B. $2\sqrt{21}$
• C. $21\sqrt{12}$
• D. $10+2\sqrt{21}$

Answer 1

The correct option is D $10+2\sqrt{21}$

$(\sqrt{7}+\sqrt{3}{)}^2$
=$(\sqrt{7}+\sqrt{3})(\sqrt{7}+\sqrt{3})$
Using distributive property, we get
=$\sqrt{7}(\sqrt{7}+\sqrt{3})+\sqrt{3}(\sqrt{7}+\sqrt{3})$
=$(\sqrt{7}\times \sqrt{7})+(\sqrt{7}\times \sqrt{3})+(\sqrt{7}\times \sqrt{3})+(\sqrt{3}\times \sqrt{3})$
=$7+\sqrt{21}+\sqrt{21}+3$
=$10+2\sqrt{21}$.

So, option $D$ is correct.