Question

express in simplest radical form.

$-3\sqrt{90} - \sqrt{10}$

Explanation:

Step1: Simplify \(\sqrt{90}\)

We factor 90 to find perfect square factors. \(90 = 9\times10\), and \(\sqrt{9\times10}=\sqrt{9}\times\sqrt{10}=3\sqrt{10}\) (since \(\sqrt{9} = 3\)).

Step2: Substitute back into the expression

The original expression is \(-3\sqrt{90}-\sqrt{10}\). Substituting \(\sqrt{90}=3\sqrt{10}\), we get \(-3\times(3\sqrt{10})-\sqrt{10}\).

Step3: Simplify the first term

\(-3\times(3\sqrt{10})=-9\sqrt{10}\). So now the expression is \(-9\sqrt{10}-\sqrt{10}\).

Step4: Combine like terms

Since both terms have \(\sqrt{10}\), we can combine the coefficients: \((-9 - 1)\sqrt{10}=-10\sqrt{10}\).

Answer:

\(-10\sqrt{10}\)