Question

simplify.
\sqrt{18} + 5\sqrt{98}

Explanation:

Step1: Simplify each square root

Factor the radicands: \(18 = 9\times2\), \(98 = 49\times2\).
So, \(\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}\) (since \(\sqrt{9}=3\)).
And \(5\sqrt{98}=5\sqrt{49\times2}=5\times\sqrt{49}\times\sqrt{2}=5\times7\times\sqrt{2}=35\sqrt{2}\) (since \(\sqrt{49}=7\)).

Step2: Combine like terms

Now we have \(3\sqrt{2}+35\sqrt{2}\). Since both terms have \(\sqrt{2}\), we add the coefficients: \(3 + 35 = 38\).
So, \(3\sqrt{2}+35\sqrt{2}=38\sqrt{2}\).

Answer:

\(38\sqrt{2}\)