Numbers can be categorized into subsets called rational and irrational numbers. An example of irrational numbers are decimals that have no end or are non-terminating. A common confusion is that because a decimal has no end it is a large number that tends to infinity, whereas that isn’t true.
Take a look at the exponential constant e, e has a value of 2.7182818… and is non-terminating but not a huge value because at the end of the day e will never be greater than 3. On the other hand, rational numbers are decimals that can be written as fractions that divide two integers (as long as the denominator is not 0). Thus, for this problem, since the square root of 24, or 4.899, is a non-terminating decimal, so the square root of 24 is irrational.
24 is NOT a perfect square. 24 is a natural number, but since there is no other natural number that can be squared to result in the number 24, 24 is NOT a perfect square.
Step 1: Find the prime factors of the number inside the radical sign. Step 2: Group the factors into pairs. Step 3: Pull out one integer outside the radical sign for each pair. Leave the other integers that could not be paired inside the radical sign.
Flexi Says: The square root of a number is rational if it can be expressed as a fraction of two integers, and irrational if it cannot. The square root of 24 is approximately 4.90, which is not a perfect square and therefore is an irrational number.
The square root of 24 is approximately 4.899. Rounding it to the nearest whole numbers, we get 4 and 5. So, the square root of 24 lies between 4 and 5. In other words, 4 < √24 < 5.
The square root of 24 is a mathematical expression represented as √24. In its simplest radical form, it is expressed as 2√6, and in decimal form, it's approximately 4.898979485.
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