Question

subtract. write your answer in simplest form.
$-3sqrt{10} - 10sqrt{90}$

Explanation:

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

We know that \(90 = 9\times10\), so \(\sqrt{90}=\sqrt{9\times10}\). By the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{9\times10}=\sqrt{9}\times\sqrt{10} = 3\sqrt{10}\).

Step2: Substitute back into the original expression

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

Step3: Simplify the expression

First, calculate \(10\times(3\sqrt{10})=30\sqrt{10}\). Then the expression becomes \(-3\sqrt{10}-30\sqrt{10}\). Since the terms are like radicals (both have \(\sqrt{10}\)), we can combine them: \((-3 - 30)\sqrt{10}=-33\sqrt{10}\).

Answer:

\(-33\sqrt{10}\)