How do you simplify √294?

To simplify the square root of 294, we start by finding its prime factors. This helps us break it down into simpler components.

Step 1: Factor 294

First, we can divide 294 by the smallest prime numbers:

• 294 is even, so divide by 2: 294 ÷ 2 = 147
• Next, factor 147: 147 ÷ 3 = 49
• Finally, factor 49: 49 = 7 × 7

Step 2: Write the Prime Factorization

The complete prime factorization of 294 is:

2 × 3 × 7 × 7

Step 3: Simplify the Square Root

Now, we can simplify the square root:

Since there are two 7s, we can take one 7 out of the square root:

√294 = √(2 × 3 × 7 × 7) = 7√(2 × 3) = 7√6

Final Result

The simplified form of √294 is:

7√6