# The Square Root of 24: An Explanation

As a math student, you may often come across various mathematical concepts that seem daunting and challenging to understand. One such concept is the square root of 24. In this article, we will take an in-depth look at what the square root of 24 is, how to find it, and its significance.

Firstly, we need to understand what a square root is. A square root is a number that, when multiplied by itself, gives the original number as the product. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9. The symbol used to represent square roots is √. So, in mathematical terms, the square root of 9 is represented as √9.

Now, let us proceed to the square root of 24. To find the square root of 24, we must determine the number that, when multiplied by itself, gives 24. Unfortunately, we cannot express the square root of 24 as a whole number or fraction. Instead, we must resort to approximations. One way to approximate the square root of 24 is to use the long division method.

To begin with, we split 24 into two-digit blocks starting from the right. In this case, 24 only has one digit, so we add a zero to get 240. We then find a number that can be squared and subtracted from 240. To do this, we start by guessing a number that we know is less than the square root of 240. Let’s use the number 14.

We square 14 to get 196. Then, we subtract 196 from 240, leaving us with 44. We bring down another zero from 24 to get 440. We then double the number 14, which gives us 28. We place 2 before the decimal point as the first decimal place. We then guess a number that, when added to 28, gives us a value less than or equal to 440. In this case, let’s try 3.

We then multiply 283 by 3 to get 849. We subtract 849 from 4400, leaving us with 3551. We add another zero from 24 to get 35510. We double 283, which gives us 566. We place 5 before the decimal point as the second decimal place. We repeat the process of guessing and multiplying until we have obtained the degree of accuracy that we require.

Using this method, we can say that the square root of 24 is approximately 4.899. However, this is just an approximation, and the actual value of the square root of 24 is irrational and never-ending.

So, why is the square root of 24 significant? First and foremost, it is essential in Trigonometry because it is involved in various trigonometric functions such as sine, cosine, and tangent. For instance, the sine of 30 degrees is 0.5, and the cosine of 60 degrees is 0.5. These values are related to the square root of 24.

Furthermore, the square root of 24 is also crucial in Geometry, specifically in the construction of the regular heptagon (a seven-sided polygon). The construction of a regular heptagon involves using numbers associated with the square root of 24. The Greeks used this calculation to construct heptagons precisely, which was critical in developing their geometric knowledge.

In conclusion, the square root of 24 is a fundamental mathematical concept that has essential applications in various fields of mathematics. While we cannot express it as a whole number or fraction, we can approximate it using long division. Its significance in Trigonometry and Geometry makes it a valuable concept to understand as a math student.