What is the square root of 6561?
Understand the Problem
The question is asking for the square root of 6561. To solve this, we need to determine which number, when multiplied by itself, equals 6561.
Answer
$81$
Answer for screen readers
The square root of 6561 is $81$.
Steps to Solve
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Identify the square root To find the square root of 6561, we need to look for a number $x$ such that $x^2 = 6561$.
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Estimate the range First, we can estimate the range by considering the square of numbers around 80, since $80^2 = 6400$ and $90^2 = 8100$. This tells us that the square root is between 80 and 90.
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Narrow down the estimate Let's try squaring 81: $$ 81^2 = 81 \times 81 = 6561 $$ Now we see that $6561$ equals $81^2$.
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Conclusion Since we found that $81 \times 81 = 6561$, we conclude that the square root of 6561 is $81$.
The square root of 6561 is $81$.
More Information
The square root is a fundamental concept in mathematics, and the square root of 6561 is notably used in various mathematical operations and applications, often appearing in educational settings. Did you know that 6561 is also a power of 3, specifically $3^8$?
Tips
- Confusing square roots with cubes: Ensure you are calculating the square root (a number multiplied by itself) and not the cube root (a number multiplied by itself twice).
- Forgetting that both positive and negative numbers can be square roots: In this case, 81 is the principal square root.
