between which two square roots of integers can you find pi?

You can find π (or pi) between square roots √9 and √10

since 3 < pi < 4,

√9 < pi √16

In fact, since pi^2 = 9.86,

√9 < pi < √10

Pi is between the square root of 9 and 10

To determine between which two square roots of integers you can find pi, let's first establish that pi is an irrational number. This means it cannot be expressed as a fraction or the square root of an integer. However, we can approximate the value of pi using various methods.

One well-known method is to use the infinite series expansion of pi. One such series is the Leibniz series, which alternates positive and negative terms:

Pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

By adding up more terms in this series, we can obtain increasingly accurate approximations of pi. The series converges slowly, so it requires many terms to get a high level of precision.

To find the square roots of integers that can approximate pi, we can square both sides of this equation:

Pi^2/16 = (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...)^2

Simplifying this equation, we have:

Pi^2/16 = 1 - 2/3 + 1/9 - 2/15 + 1/25 - 2/35 + ...

Now, we can take the square root of both sides:

Pi/4 = √(1 - 2/3 + 1/9 - 2/15 + 1/25 - 2/35 + ...)

However, it is important to note that this expression is an approximation of pi, not an exact representation. Therefore, there is no specific pair of square roots of integers between which we can find pi.