What is the square root of 1296?
Understand the Problem
The question is asking for the square root of the number 1296. To find the square root, we need to determine which number, when multiplied by itself, equals 1296.
Answer
The square root of 1296 is $36$.
Answer for screen readers
The square root of 1296 is $36$.
Steps to Solve
- Identify the square root definition
The square root of a number $x$ is a value $y$ such that $y^2 = x$. Here, we need to find a number $y$ such that $y^2 = 1296$.
- Start estimating the square root
We can start estimating the square root by finding two perfect squares around 1296. We know that $30^2 = 900$ and $40^2 = 1600$. This means the square root of 1296 is between 30 and 40.
- Narrow down the estimation
Next, we try numbers between 30 and 40:
- $35^2 = 1225$
- $36^2 = 1296$
- $37^2 = 1369$
From this, we find that $36^2 = 1296$.
- Conclude the solution
Since we found that $36 \times 36 = 1296$, we conclude that:
$$ \sqrt{1296} = 36 $$
The square root of 1296 is $36$.
More Information
The value 1296 is a perfect square, which means its square root is an integer. Perfect squares are numbers that result from squaring an integer. The next perfect square after 1296 is 1369, which is $37^2$.
Tips
- A common mistake is incorrectly estimating between two numbers. It’s important to square the estimated numbers to check if they fall around the target number.
- Another mistake might be skipping the checking step and assuming the first guess is correct without verifying by squaring.
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