What is the square root of 1600?
The Correct Answer and Explanation is :
The square root of 1600 is 40.
Explanation:
To understand why, let’s break down what square roots are. A square root is a number that, when multiplied by itself, gives the original number. In mathematical terms, the square root of a number ( x ) is the number ( y ) such that:
[
y^2 = x
]
In this case, we’re looking for a number that, when multiplied by itself, results in 1600. That means:
[
y^2 = 1600
]
Now, to find the square root of 1600, we need to determine which number, when multiplied by itself, equals 1600.
Step-by-Step Process:
- Start by guessing a number close to the square root of 1600. Since 1600 is a relatively round number, it might be helpful to remember that 40 times 40 equals 1600.
- Let’s do the multiplication:
[
40 \times 40 = 1600
]
Since this is true, we can confidently say that the square root of 1600 is 40.
Why the Square Root Works:
The square root function essentially “reverses” the process of squaring a number. Squaring means multiplying a number by itself, while the square root is finding the original number that, when squared, results in the given number. For example:
[
\sqrt{1600} = 40 \quad \text{because} \quad 40^2 = 1600
]
The square root of a number is always non-negative by definition. For instance, ( \sqrt{1600} = 40 ), while ( -40 \times -40 = 1600 ), but the principal (positive) square root is typically used in most contexts, especially for simplicity.
Conclusion:
So, the square root of 1600 is 40, and this is derived from understanding that the square root function is the inverse of squaring a number.