Question

5 multiply \\(sqrt{x} (3sqrt{x} + sqrt{x})\\). use this (copy and paste) for your radical symbol_ √ *no parentheses are needed

Explanation:

Step1: Apply distributive property

Using the distributive property \(a(b + c)=ab + ac\), where \(a = \sqrt{x}\), \(b = 3\sqrt{x}\), and \(c=\sqrt{x}\), we get \(\sqrt{x}\times3\sqrt{x}+\sqrt{x}\times\sqrt{x}\).

Step2: Multiply the radicals

For \(\sqrt{x}\times3\sqrt{x}\), we use the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) (here \(a = b = x\)), so \(\sqrt{x}\times\sqrt{x}=x\), and then \(3\times x = 3x\). For \(\sqrt{x}\times\sqrt{x}\), we get \(x\).

Step3: Combine like terms

Adding \(3x\) and \(x\) gives \(4x\).

Answer:

\(4x\)