Question

1. $4sqrt{112} - 2sqrt{175}$

Explanation:

Step1: Simplify each square root

For \(4\sqrt{112}\), factor 112: \(112 = 16\times7\), so \(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\). Then \(4\sqrt{112}=4\times4\sqrt{7}=16\sqrt{7}\).
For \(2\sqrt{175}\), factor 175: \(175 = 25\times7\), so \(\sqrt{175}=\sqrt{25\times7}=5\sqrt{7}\). Then \(2\sqrt{175}=2\times5\sqrt{7}=10\sqrt{7}\).

Step2: Subtract the simplified terms

Now we have \(16\sqrt{7}-10\sqrt{7}\). Since the radicals are the same, we subtract the coefficients: \((16 - 10)\sqrt{7}=6\sqrt{7}\).

Answer:

\(6\sqrt{7}\)