Question

What is the value of $\sqrt[2]{28}$ + $\sqrt[2]{218}$ ?

• A. $5\sqrt[2]{25}$
• B. $\sqrt[2]{22}$
• C. $5\sqrt[2]{22}$
• D. $3\sqrt[2]{22}$

Answer 1

The correct option is C

$5\sqrt[2]{22}$

Both surds are in the same order. Now we need to express them in their simplest form.

$\sqrt[2]{28}$ = $\sqrt[2]{24\times 2}$ = $\sqrt[2]{22^2\times 2}$ = $2\sqrt[2]{22}$

$\sqrt[2]{218}$ = $\sqrt[2]{29\times 2}$ = $\sqrt[2]{23^2\times 2}$ = $3\sqrt[2]{22}$

$2\sqrt[2]{22}$ + $3\sqrt[2]{22}$ = $5\sqrt[2]{22}$