Question

√(8x) + 5√(2x)
a 14x
b 7√x
c 7√(4x)
d 7√(2x)

Explanation:

Step1: Simplify \(\sqrt{8x}\)

We know that \(8 = 4\times2\), so \(\sqrt{8x}=\sqrt{4\times2x}\). By the property of square roots \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{4\times2x}=\sqrt{4}\cdot\sqrt{2x}\). Since \(\sqrt{4} = 2\), then \(\sqrt{8x}=2\sqrt{2x}\).

Step2: Combine like terms

Now we have the expression \(\sqrt{8x}+5\sqrt{2x}\), substituting the simplified form of \(\sqrt{8x}\) we get \(2\sqrt{2x}+5\sqrt{2x}\). Since \(2\sqrt{2x}\) and \(5\sqrt{2x}\) are like terms (they have the same radical part \(\sqrt{2x}\)), we can combine them by adding their coefficients: \((2 + 5)\sqrt{2x}=7\sqrt{2x}\).

Answer:

D. \(7\sqrt{2x}\)