Question

simplify $3sqrt{13} + 7sqrt{13}$.

Explanation:

Step1: Recognize like radicals

Both terms have $\sqrt{13}$, so we can combine them using the distributive property (reverse of factoring). The formula for combining like radicals is $a\sqrt{b} + c\sqrt{b} = (a + c)\sqrt{b}$. Here, $a = 3$, $c = 7$, and $b = 13$.

Step2: Add the coefficients

Add the coefficients 3 and 7: $3 + 7 = 10$.

Step3: Combine with the radical

Using the formula from Step 1, we get $(3 + 7)\sqrt{13} = 10\sqrt{13}$.

Answer:

$10\sqrt{13}$