Question

subtract. write your answer in simplest form.
$-9\sqrt{40} - 3\sqrt{10}$

Explanation:

Step1: Simplify \(\sqrt{40}\)

Factor 40: \(40 = 4\times10\), so \(\sqrt{40}=\sqrt{4\times10}=\sqrt{4}\times\sqrt{10}=2\sqrt{10}\) (since \(\sqrt{4} = 2\)).

Step2: Substitute back into the original expression

The original expression is \(-9\sqrt{40}-3\sqrt{10}\). Substitute \(\sqrt{40}=2\sqrt{10}\):
\(-9\times(2\sqrt{10})-3\sqrt{10}=-18\sqrt{10}-3\sqrt{10}\)

Step3: Combine like terms

Combine the terms with \(\sqrt{10}\): \(-18\sqrt{10}-3\sqrt{10}=(-18 - 3)\sqrt{10}=-21\sqrt{10}\)

Answer:

\(-21\sqrt{10}\)