How do you simplify √128?

To simplify the square root of 128, follow these steps:

Breaking Down the Number

First, factor 128 into its prime components:

• 128 = 64 × 2
• 64 = 8 × 8
• 8 = 4 × 2
• 4 = 2 × 2

Identifying Perfect Squares

From the factorization, we can see that 64 is a perfect square:

• √64 = 8

Combining the Results

Now, we can rewrite √128 using its factors:

√128 = √(64 × 2) = √64 × √2

Simplifying Further

Now substitute the value of √64:

√128 = 8√2

Final Answer

The simplified form of √128 is 8√2.