Question

add. write your answer in simplest form.
$-9sqrt{56} + sqrt{14}$

Explanation:

Step1: Simplify \(\sqrt{56}\)

Factor 56: \(56 = 4\times14\), so \(\sqrt{56}=\sqrt{4\times14}=\sqrt{4}\times\sqrt{14}=2\sqrt{14}\).

Step2: Substitute back into the expression

The original expression is \(-9\sqrt{56}+\sqrt{14}\). Substitute \(\sqrt{56}=2\sqrt{14}\), we get \(-9\times2\sqrt{14}+\sqrt{14}\).

Step3: Simplify the terms

Calculate \(-9\times2\sqrt{14}=-18\sqrt{14}\), so the expression becomes \(-18\sqrt{14}+\sqrt{14}\).

Step4: Combine like terms

Combine \(-18\sqrt{14}\) and \(\sqrt{14}\): \((-18 + 1)\sqrt{14}=-17\sqrt{14}\).

Answer:

\(-17\sqrt{14}\)