Question

subtract. write your answer in simplest form
$-9\sqrt{2} - 4\sqrt{98}$

Explanation:

Step1: Simplify \(\sqrt{98}\)

We know that \(98 = 49\times2\), so \(\sqrt{98}=\sqrt{49\times2}\). By the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 49\), \(b = 2\) and \(a\geq0,b\geq0\)), we have \(\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}\).

Step2: Substitute back and simplify the expression

The original expression is \(- 9\sqrt{2}-4\sqrt{98}\). Substitute \(\sqrt{98} = 7\sqrt{2}\) into the expression, we get \(-9\sqrt{2}-4\times(7\sqrt{2})\).
First, calculate \(4\times7 = 28\), so the expression becomes \(-9\sqrt{2}-28\sqrt{2}\).
Now, combine like terms. Since both terms have \(\sqrt{2}\), we can factor out \(\sqrt{2}\): \((-9 - 28)\sqrt{2}\).
Calculate \(-9-28=-37\), so the expression simplifies to \(-37\sqrt{2}\).

Answer:

\(-37\sqrt{2}\)