Question

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

Explanation:

Step1: Simplify each square root

First, simplify $\sqrt{28}$ and $\sqrt{112}$.
For $\sqrt{28}$, we can factor 28 as $4\times7$, so $\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}$.
For $\sqrt{112}$, factor 112 as $16\times7$, so $\sqrt{112}=\sqrt{16\times7}=\sqrt{16}\times\sqrt{7}=4\sqrt{7}$.

Step2: Substitute back into the original expression

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

Step3: Perform the multiplications

Calculate the multiplications: $-9\times2\sqrt{7}=-18\sqrt{7}$ and $-7\times4\sqrt{7}=-28\sqrt{7}$.

Step4: Combine like terms

Now, combine the two terms: $-18\sqrt{7}-28\sqrt{7}=(-18 - 28)\sqrt{7}=-46\sqrt{7}$.

Answer:

$-46\sqrt{7}$