What is the square root of 9801?
Understand the Problem
The question is asking to find the square root of the number 9801. This involves determining which number, when multiplied by itself, equals 9801.
Answer
$99$
Answer for screen readers
The final answer is $\sqrt{9801} = 99$.
Steps to Solve
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Identify the equation for square root To find the square root of 9801, we need to find a number $x$ such that: $$ x^2 = 9801 $$
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Estimate the square root To estimate the square root of 9801, we can find two perfect squares close to 9801. For example, $90^2 = 8100$ and $100^2 = 10000$. So, we know $\sqrt{9801}$ is between 90 and 100.
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Calculate the square root Now we can calculate the exact square root of 9801. Since we know it's between 90 and 100, let's try some values:
- $95^2 = 9025$
- $96^2 = 9216$
- $97^2 = 9409$
- $98^2 = 9604$
- $99^2 = 9801$
We find that: $$ 99^2 = 9801 $$
- Conclude the solution From our calculations, we find that: $$ \sqrt{9801} = 99 $$
The final answer is $\sqrt{9801} = 99$.
More Information
The number 9801 is a perfect square, specifically $99^2$. Knowing that certain numbers are perfect squares can help in quickly identifying square roots.
Tips
- Overlooking perfect squares: Some might not recognize 9801 as a perfect square at first. It’s important to check nearby perfect squares systematically.
- Incorrect calculations: Errors in basic multiplication can lead to incorrect conclusions about the square root.
