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

$16$

Steps to Solve

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 $x^2 = 256$.
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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