What is the square root of 76?
Understand the Problem
The question is asking for the square root of the number 76, which involves finding a value that, when multiplied by itself, equals 76.
Answer
The square root of 76 is approximately $8.7178$.
Answer for screen readers
The square root of 76 is approximately $8.7178$.
Steps to Solve
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Calculate the Square Root We need to find a number $x$ such that $x^2 = 76$. This number, $x$, is the square root of 76.
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Use a Calculator or Approximation Method To find the square root of 76, you can use a calculator. Alternatively, if you're estimating:
- We know $8^2 = 64$ and $9^2 = 81$.
- The square root of 76 falls between 8 and 9.
- Calculate the Exact Value Using a calculator or doing a more precise estimation will give us: $$ \sqrt{76} \approx 8.7178 $$
The square root of 76 is approximately $8.7178$.
More Information
The square root of a number is a value that, when squared (multiplied by itself), returns the original number. In this case, $8.7178 \times 8.7178 \approx 76$. Square roots can be irrational numbers, meaning they cannot be exactly expressed as simple fractions.
Tips
- Not using a calculator for square roots: Many might try to approximate the square root without realizing they could easily use a calculator for a more accurate result.
- Forgetting that square roots can be both positive and negative: While the principal square root is usually understood as the positive root, it's important to remember that both $x$ and $-x$ are valid solutions to $x^2 = 76$.
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