Question

question
simplify \\(\sqrt{49x^2}\\) completely given \\(x > 0\\).
answer attempt 1 out of 2

Explanation:

Step1: Apply square - root property

We know that for non - negative real numbers \(a\) and \(b\), \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\). So, we can rewrite \(\sqrt{49x^{2}}\) as \(\sqrt{49}\cdot\sqrt{x^{2}}\).

Step2: Simplify each square - root

We know that \(\sqrt{49} = 7\) because \(7\times7 = 49\). Also, since \(x>0\), \(\sqrt{x^{2}}=x\) (by the property that if \(a > 0\), then \(\sqrt{a^{2}}=a\)).
Then, \(\sqrt{49}\cdot\sqrt{x^{2}}=7\times x = 7x\).

Answer:

\(7x\)