Question

which of the following is equal to \\(sqrt{9 cdot 4}\\)? a. \\(sqrt{9} cdot sqrt{4}\\) b. 18 c. 36 d. \\(sqrt{\frac{9}{4}}\\)

Explanation:

Step1: Recall the property of square roots

The property of square roots states that for non - negative real numbers \(a\) and \(b\), \(\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\).
Here, \(a = 9\) and \(b = 4\), so \(\sqrt{9\cdot4}=\sqrt{9}\cdot\sqrt{4}\).
Let's also check the other options:

• Option B: Calculate \(\sqrt{9\cdot4}=\sqrt{36} = 6\), and \(18

eq6\).

• Option C: \(\sqrt{9\cdot4}=\sqrt{36}=6\), and \(36

eq6\).

• Option D: \(\sqrt{\frac{9}{4}}=\frac{3}{2}\), and \(\frac{3}{2}

eq6\).

Answer:

A. \(\sqrt{9}\cdot\sqrt{4}\)