Question

Find the square root of:

$31+4\sqrt{21}$

• A. $\sqrt{24}+\sqrt{3}$
• B. $\sqrt{28}+\sqrt{3}$
• C. $\sqrt{36}+\sqrt{3}$
• D. $\sqrt{28}+\sqrt{2}$

Answer 1

Answer: (B)

$\sqrt{28}+\sqrt{3}$

$31+4\sqrt{21}$

$=28+3+2\sqrt{4\times 21}$

$=(\sqrt{28}{)}^2+(\sqrt{3}{)}^2+2\sqrt{28}\times \sqrt{3}$

$=(\sqrt{28}+\sqrt{3}{)}^2$...........Using $(a+b{)}^2=a^2+b^2+2ab$

$31+4\sqrt{21}=(\sqrt{28}+\sqrt{3}{)}^2$

$\therefore \sqrt{31+4\sqrt{21}}=(\sqrt{28}+\sqrt{3})$

The square root of $\sqrt{31+4\sqrt{21}}$ is $(\sqrt{28}+\sqrt{3})$