Question

what is the following sum?
$4\sqrt{5}+2\sqrt{5}$
options:
$8\sqrt{10}$
$6\sqrt{10}$
$6\sqrt{5}$
$8\sqrt{5}$

Explanation:

Step1: Identify like radicals

The expression is \(4\sqrt{5} + 2\sqrt{5}\). Both terms have the same radical part \(\sqrt{5}\), so they are like radicals.

Step2: Add the coefficients

For like radicals \(a\sqrt{b}+c\sqrt{b}=(a + c)\sqrt{b}\). Here, \(a = 4\), \(c = 2\), and \(b = 5\). So, \(4+2 = 6\), and the sum is \(6\sqrt{5}\).

Answer:

\(6\sqrt{5}\) (corresponding to the option with \(6\sqrt{5}\))