What is the square root of pi?
Understand the Problem
The question is asking for the square root of the mathematical constant pi (approximately 3.14159). This requires calculating the value which, when multiplied by itself, equals pi.
Answer
$\sqrt{\pi} \approx 1.77245$
Answer for screen readers
$\sqrt{\pi} \approx 1.77245$
Steps to Solve
- Recall the definition of square root
The square root of a number $x$ is a value $y$ such that $y * y = x$ or $y^2 = x$.
- Approximate the value of $\pi$
We know that $\pi \approx 3.14159$.
- Estimate the square root of $\pi$
Since $1.7 * 1.7 = 2.89$ and $1.8 * 1.8 = 3.24$, we can estimate that $\sqrt{\pi}$ is between $1.7$ and $1.8$.
- Calculate the square root of $\pi$
Using a calculator, we find that $\sqrt{\pi} \approx 1.77245$.
$\sqrt{\pi} \approx 1.77245$
More Information
The square root of $\pi$ is an irrational number, meaning its decimal representation neither terminates nor repeats. It's a transcendental number as well, meaning it is not the root of any non-zero polynomial equation with rational coefficients.
Tips
A common mistake is to confuse $\pi$ with its approximation (e.g. 3.14 or 22/7) and calculate the square root of the approximation instead of $\pi$ itself, leading to a slightly different result. Rounding errors can occur if you don't use enough decimal places during calculation.
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