Question

subtract. write your answer in simplest form.
-9√28 - 7√112

Explanation:

Step1: Simplify each square root

First, simplify \(\sqrt{28}\). We know that \(28 = 4\times7\), so \(\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}\). Then, simplify \(\sqrt{112}\). Since \(112 = 16\times7\), \(\sqrt{112}=\sqrt{16\times7}=\sqrt{16}\times\sqrt{7}=4\sqrt{7}\).

Step2: Substitute back into the original expression

Substitute the simplified square roots into \(-9\sqrt{28}-7\sqrt{112}\). We get \(-9\times2\sqrt{7}-7\times4\sqrt{7}\).

Step3: Perform the multiplications

Calculate \(-9\times2\sqrt{7}=-18\sqrt{7}\) and \(7\times4\sqrt{7}=28\sqrt{7}\), so the expression becomes \(-18\sqrt{7}-28\sqrt{7}\).

Step4: Combine like terms

Since both terms have \(\sqrt{7}\), we can combine them: \((-18 - 28)\sqrt{7}=-46\sqrt{7}\).

Answer:

\(-46\sqrt{7}\)