Step-by-step explanation:
To simplify the expression \(\sqrt{4 \times 9 \times 7 \div 2 \times 3}\), follow these steps:
1. **Calculate the value inside the square root:**
\[
4 \times 9 = 36
\]
\[
36 \times 7 = 252
\]
\[
252 \div 2 = 126
\]
\[
126 \times 3 = 378
\]
2. **Take the square root of the result:**
\[
\sqrt{378}
\]
3. **Simplify the square root if possible:**
Let's break down 378 into its prime factors to simplify:
\[
378 = 2 \times 3^3 \times 7
\]
The simplified form is:
\[
\sqrt{378} = \sqrt{2 \times 3^3 \times 7}
\]
\[
= \sqrt{2} \times \sqrt{3^2 \times 3} \times \sqrt{7}
\]
\[
= 3 \sqrt{2 \times 3 \times 7}
\]
\[
= 3 \sqrt{42}
\]
So, the simplified expression is \(3\sqrt{42}\).
