Question

subtract. write your answer in simplest form.
$-sqrt{35} - 8sqrt{140}$

Explanation:

Step1: Simplify \(\sqrt{140}\)

Factor 140: \(140 = 4\times35\), so \(\sqrt{140}=\sqrt{4\times35}\). By property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{4\times35}=\sqrt{4}\cdot\sqrt{35}=2\sqrt{35}\).

Step2: Substitute back into the expression

The original expression is \(-\sqrt{35}-8\sqrt{140}\). Substitute \(\sqrt{140}=2\sqrt{35}\), we have \(-\sqrt{35}-8\times(2\sqrt{35})\).

Step3: Simplify the coefficient

Calculate \(8\times2 = 16\), so the expression becomes \(-\sqrt{35}-16\sqrt{35}\).

Step4: Combine like terms

Since both terms have \(\sqrt{35}\), we combine the coefficients: \((-1 - 16)\sqrt{35}=-17\sqrt{35}\).

Answer:

\(-17\sqrt{35}\)