simplify square root of 256
Understand the Problem
The question is asking us to simplify the square root of 256, which involves finding a number that, when multiplied by itself, gives us 256.
Answer
$16$
Answer for screen readers
The square root of 256 is $16$.
Steps to Solve
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Identify the Square Root To find the square root of 256, we need to find a number that, when multiplied by itself, equals 256. We are looking for $x$ such that $x^2 = 256$.
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Find the Factor Pairs We can identify the pairs of factors of 256. The pairs are:
- $1 \times 256$
- $2 \times 128$
- $4 \times 64$
- $8 \times 32$
- $16 \times 16$
- Determine the Square Root Among the factor pairs, the pair $16 \times 16 = 256$ indicates that $16$ multiplied by itself is $256$, hence the square root is: $$ \sqrt{256} = 16 $$
The square root of 256 is $16$.
More Information
The square root of a number is one of the most fundamental operations in mathematics. The number 256 is a perfect square, meaning its square root is an integer. Understanding square roots is essential for more advanced algebra and geometry.
Tips
- Misidentifying Non-Perfect Squares: Sometimes students confuse numbers that are not perfect squares with perfect squares. Always check if both factors are equal to find perfect squares.
- Incorrect Calculations: Be careful when multiplying the factors; verify your calculations to ensure they sum to the correct product.
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