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Slimlify : √4×9×7÷2×3

Sagot :

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 \(3\sqrt{42}\).