Question

timed problem
score: 6/10 current time: 14:20
select the most simplified equivalent.
\\(\sqrt{5} + \sqrt{2}\\)
answer
\\(2\sqrt{7}\\)
\\(\sqrt{5} + \sqrt{2}\\)
\\(\sqrt{7}\\)

Explanation:

Step1: Identify like radicals rule

Only radicals with identical radicands can be combined.

Step2: Analyze the expression

$\sqrt{5}$ and $\sqrt{2}$ have different radicands (5 and 2), so they cannot be added or simplified further into a single radical or a combined term with a single radical.

Step3: Evaluate other options

$2\sqrt{7}$ and $\sqrt{7}$ do not match the value of $\sqrt{5}+\sqrt{2}$, as $\sqrt{5}+\sqrt{2}\approx2.236+1.414=3.65$, while $2\sqrt{7}\approx5.29$ and $\sqrt{7}\approx2.65$.

Answer:

$\sqrt{5}+\sqrt{2}$