Maximum Value Identification: Comparing Numerical Options

Choose the largest value

To determine which of the suggested options has the largest numerical value, we will use the definition of root as a power:

$\sqrt[n]{a}=a^{\frac{1}{n}}$Let's substitute each one of the square roots in the suggested options with powers:

$\sqrt{2}\rightarrow2^{\frac{1}{2}}\\ \sqrt{3}\rightarrow3^{\frac{1}{2}}\\ \sqrt{4}\rightarrow4^{\frac{1}{2}}\\ \sqrt{5}\rightarrow5^{\frac{1}{2}}\\$Now let's note that all the expressions we got have the same exponent (and their bases are positive, we'll also mention, although it's obvious), therefore we can determine the trend between them using only the trend between their bases, since it's identical to it:

$5>4>3>2\hspace{4pt} (>0)\\ \downarrow\\ 5^{\frac{1}{2}}>4^{\frac{1}{2}} >3^{\frac{1}{2}}>2^{\frac{1}{2}}$In other words, we got that:

$\sqrt{5}>\sqrt{4}>\sqrt{3}>\sqrt{2}$Therefore the correct answer is answer D.