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Can you approximate irrational numbers? How?
See solution.
sqrt(16) < sqrt(23) < sqrt(25) ⇕ 4 < sqrt(23) < 5 We found that sqrt(23) is somewhere between 4 and 5. However, the two other numbers we want to compare it with are also between 4 and 5, which means that we need a better approximation. Let's use decimals. Let's see if sqrt(23) is greater than 4.5. 4.5 * 4.5 = 20.25 4.5 < sqrt(23) < 5 Now we know that sqrt(23) is somewhere between 4.5 and 5, which is a better approximation. Let's approximate 4.205639 ... as a rational number by rounding it to the nearest tenth. 4.205639 ... ≈ 4.2 Finally, we can plot each number on a number line to compare them. We know that sqrt(23) is somewhere between 4.5 and 5, so we will plot it between these numbers.
As we can see, to compare rational and irrational numbers, we must first find rational approximations of the irrational numbers. We can do this using perfect squares or by rounding.