Question

Compare the following pair of surds:

$\sqrt{5},\sqrt{6}$

• A. $\sqrt{5}<\sqrt{6}$
• B. $\sqrt{4}<\sqrt{6}$
• C. $\sqrt{5}>\sqrt{3}$
• D. $\sqrt{2}<\sqrt{6}$

Answer 1

Answer: (A)

$\sqrt{5}<\sqrt{6}$

$\sqrt{5},\sqrt{6}$
The order of the surds are similar. Thus, we can compare the surds.
$5<6$
$⟹5^{\frac{1}{2}}<6^{\frac{1}{2}}$
$⟹\sqrt{5}<\sqrt{6}$