Square roots are found in many science and maths problems, and students must know the basics of square roots to tackle many questions. Square roots are indispensable in various fields like calculus, engineering and virtually every career path of the modern world. Solving equations involving square roots is an important skill in algebra, so kids must understand the simple square root concept.
Basically, the square root is a number that when multiplied by itself provides the original number. For example, the square root of 100 is 10 and the square root of 0 is 0. Also, every root has a positive and a negative answer, so the square root of 4 = 2 and also -2. This is because 2 squared is four and -2 squared is also 4. But most kids tend to remember the positive answer only. So, √4 = ±2, with the ± standing in for “plus or minus.” Although answering just 2 is acceptable in many cases, particularly when a negative answer does not make sense for the intended application. For example, if the solution to the square root is the answer to a question involving dimensions of a prism, only the positive solution is applicable.
Why is this simple concept so often forgotten?
A lot of kids forget this concept since they are introduced to negative numbers later on in their schooling and different topics are segregated in primary school and early high school. This makes it hard for students to integrate topics as they progress to more advanced levels of mathematics. My theory is, students learning about surds will no doubt be explicitly taught about the plus/minus answer and remember to apply it, but then set that knowledge aside when learning about polynomials or algebra.
How to help students remember this outside of its direct teaching?
It is essential for us to remind our kids that the answer to a positive number's square root will always have both a positive and negative solution.
As students tackle problems independently, they are likely to make mistakes by omitting neative solutions. As they study, they are likely to learn from these mistakes and begin to make them less often. This is why it is so essential for students to learn and practice a variety of study techniques as part of their homework routine from a young age. With the recent return to school, teachers can begin introducing positive study techniques and habits into their daily classroom routine.
Similarly, we should emphasise that negative number do not have real square roots, because a real number cannot yield a negative value when multiplied by itself. Therefore, a negative square root of a positive number is often ignored. For example, they will give an answer for the square root of 361 as 19 rather than -19 and 19.
It is important for students to understand that the negative root exists, but the positive answer is often the preferred choice.
Overall, kids often forget this concept, so parents and teachers must make an extra effort to remind that every number will always have two roots – a positive and negative. It is then up to them to answer the question with consideration to the practical application.