what’s the square root of 71
What is the square root of 71?
Answer: The square root of 71 is an irrational number, which means it cannot be expressed exactly as a simple fraction. Instead, it has an infinite number of non-repeating decimal places.
Approximate Value
The approximate value of the square root of 71 is:
\sqrt{71} \approx 8.426149773
Finding the Square Root
To find the square root of a number, you can use several methods, including:
1. Long Division Method:
- This method involves a step-by-step approach to get the approximate value of the square root. It is time-consuming but provides a very accurate result.
2. Estimation Method:
- Find the nearest perfect squares to 71. We know that 64 (which is 8^2) and 81 (which is 9^2) are the nearest perfect squares.
- Thus, \sqrt{64} < \sqrt{71} < \sqrt{81} implies 8 < \sqrt{71} < 9.
- Refine this by trial and error or more systematic methods to hone in on the decimal value.
3. Using a Calculator:
- The most straightforward method is to use a scientific calculator, which will provide a more precise value.
Verification
To verify the accuracy of an approximated square root, simply square the approximation. For example:
8.426149773^2 \approx 71
Mathematical Expression:
In mathematical notation:
\sqrt{71}
Significance in Problems:
Knowing the square root of numbers like 71 is particularly important in fields such as engineering, physics, and any scientific computations where precise values are necessary.
By understanding these methods, students can develop a better grasp of how to approach finding and verifying square roots, whether using manual calculations or technological tools.