Question

3 what is \\(\sqrt{72}\\) expressed in simplest radical form?

1. \\(2\sqrt{18}\\)
2. \\(3\sqrt{8}\\)
3. \\(6\sqrt{2}\\)
4. \\(8\sqrt{3}\\)

4 when \\(\sqrt{72}\\) is expressed in simplest \\(a\sqrt{b}\\) form, what is the value of \\(a\\)?

1. 6
2. 2
3. 3
4. 8

Explanation:

Question 3

Step1: Factor 72 into perfect square and other

We know that \(72 = 36\times2\), and \(36\) is a perfect square. So, \(\sqrt{72}=\sqrt{36\times2}\).

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we have \(\sqrt{36\times2}=\sqrt{36}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{36}\)

Since \(\sqrt{36} = 6\), then \(\sqrt{36}\times\sqrt{2}=6\sqrt{2}\).

Now let's check the other options:

• Option 1: \(2\sqrt{18}\), but \(18 = 9\times2\), \(\sqrt{18}\) can still be simplified, so this is not the simplest form.
• Option 2: \(3\sqrt{8}\), and \(8 = 4\times2\), \(\sqrt{8}\) can still be simplified, so this is not the simplest form.
• Option 4: \(8\sqrt{3}\), \(\sqrt{72}\) is not equal to \(8\sqrt{3}\) because \(8\sqrt{3}=\sqrt{64\times3}=\sqrt{192}

eq\sqrt{72}\).

From question 3, we know that when \(\sqrt{72}\) is expressed in the simplest form \(a\sqrt{b}\), we have \(\sqrt{72}=6\sqrt{2}\). By comparing with the form \(a\sqrt{b}\), we can see that \(a = 6\) and \(b = 2\).

Answer:

1. \(6\sqrt{2}\)

Question 4