Square root functions are super important for physics equations of all kinds. It may be a bit hard to picture it, but square roots are some of the most useful numbers around. On a calculator, instead of the radical, you might see 'sqrt'. The number after the radical is called the radicand. The number that we want to get the root of comes after or under the tail of the radical (for example 3 if we wanted to find the square root of 3). How do we write out square roots?Ī square root equation is written out using a radical sign or radical symbol (). It's called imaginary, but it does exist to mathematicians. A complex number is a number multiplied by i. These numbers are all known as real numbers.Īll negative numbers will have a complex number as their square root. Numbers with decimals aren't perfect square roots.Īll positive numbers will have a positive number as their square root, called the principal, and a negative number. Numbers whose square roots are whole numbers, (or more accurately positive integers) are called perfect square numbers. The process of multiplying a number times itself is called squaring. So, for example, the square root of 49 is 7 (7x7=49). The square root of a number is a number that, when multiplied by itself, equals the desired value. Instead, the square root of all negative numbers is an imaginary number.What are square roots and why do we care? Any real number-whether it’s positive or negative-that is multiplied by itself is always equal to a positive number, except for 0. On the other hand, negative numbers don’t have any real square roots. What about negative numbers and zero?įor zero, it only has one square root, which is itself, 0. We mentioned earlier that any positive real numbers have two square roots, the positive one and the negative one. Square Roots of Zero and Negative Numbers Still, both irrational and rational numbers are part of real numbers, meaning they have tangible values and exist on the number line. The numbers right of the decimal 2.236067 … would continue on endlessly without any repeating pattern. The square root of 5 is an irrational number since it can’t be expressed as fractions. Rational numbers are numbers that can be expressed as fractions composed of two integers, e.g. 7/2, 50/4, and 100/3. Additionally, the square root is not even a rational number. Therefore, its square root won’t be an integer. Take a look at the equation below.ĥ is not a perfect square. If a radicand is not a perfect square, then the square root of the radicand won’t result is an integer. There are also other numbers such as 3, 5, or 13 that are referred to as imperfect squares.

Positive real numbers are not always perfect squares. In the example above, 16 is a perfect square because it has the number 4 as its square root. Perfect squares are radicands in the form of an integer, or a whole number, that has a square root of another integer. Perfect and Imperfect squaresĪs you may know, 16 is a perfect square. This way, other people can easily tell that the one who writes the equation wishes to have positive and negative numbers as the result. Instead, you can also write the equation in such a way that it explicitly indicates that you want both the positive and negative square root’s results:

While it is technically true and there's nothing wrong with it, it doesn’t tell the whole story. Most people would simply write this equation simply as. Why would we need a ± symbol in front of 4? Well, as we have discussed before, the square roots of 16 can be either 4 or (-4). The √ symbol is called the radical symbol, while the number or expression inside the symbol-in this case, 16-is called a radicand. In the equation above, you can either multiply 4 by itself or multiply (-4) by itself to get the result of 16. Writing a Square Root Equation for Positive and Negative Results In fact, should you wish to find the square root of any positive real numbers, you will get two results: the positive and negative versions of the same number. The simple answer is: yes you can get negative numbers out of square roots.

Square root of a negative number