Question

add. write your answer in simplest form.
$7\sqrt{63} + 10\sqrt{28}$

Explanation:

Step1: Simplify each square root

Factor the radicands: \(63 = 9\times7\) and \(28 = 4\times7\). Then, \(\sqrt{63}=\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}=3\sqrt{7}\) and \(\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}\).

Step2: Substitute back into the original expression

\(7\sqrt{63}=7\times3\sqrt{7}=21\sqrt{7}\) and \(10\sqrt{28}=10\times2\sqrt{7}=20\sqrt{7}\).

Step3: Add the like terms

\(21\sqrt{7}+20\sqrt{7}=(21 + 20)\sqrt{7}=41\sqrt{7}\).

Answer:

\(41\sqrt{7}\)