The general idea of square roots and their utilization in Mathematics

We can define a  square root of a number as a different number which can be found by multiplying the same number with itself. For example, the square root of 16 gives the number 4. Since multiplying the number 4 with itself, it gives the number 16. The square root is generally denoted by the symbol ‘√’. This symbol is a radical symbol and the number present within it is called a radicand. In the above example, 16 is the radicand.

When finding out the square root, there happen to be two possibilities, one positive square root and the other is a negative square root. This positive square root is sometimes defined as a principle square root. For example: √16 = ±4.

To calculate the square root of a number, we would need to find out their factors. After that, we need to group the factors to find out the result. If there are no factors available for a number, then the number is termed as an irrational number. Generally, for an irrational number, the square root would tend to decimal places which would not stop or get repeated. For example – √20 = √4 * 5= 2√5. For an irrational number – √13 = 3.60555….

Utilizing Square Roots in real-life scenarios

  1. Sometimes we tend to find houses and apartments and thus need to get the size of the plot. Advertisements over the web or in the newspaper may refer to the size as 676 square feet. It might get very tedious in finding out the solution. But if we use the formula, then we could easily find out the solution as 26*26 square feet. Thus we can get a general idea of its complete size.
  2. Eventually, in finding out the period of a pendulum, we use square roots.
  3. Pythagoras theorem mainly depends on squares and square roots. There may be a problem where there is a vertical pole and we need to find out the shadow of it being cast on the ground. We can easily calculate the following by finding out a few specific quantities and by utilizing the theorem.

Various Properties of Square Roots

  • Property 1: If a number possesses the units 2, 3, 7, and 8, then square root would not be a natural number. For example 138, 167, 248 do not have a perfect square root number.
  • Property 2: There are times when a number ends with an odd number of zeros. Here, we cannot find the square root of the number. But if the squared number has an even number of zeros, then the square root would be a number that would contain half of the zeros present within the squared number. For Example, the square root of 3000 is not possible since it has an odd number of zeros after the number. Similarly, the square root of 400 is possible and is 20 since the squared number consists of an even number of zeros.
  • Property 3: Square roots of odd numbers are always odd whereas the square roots of even numbers are always even. For example: √49 = 7. Here 49 is an odd number and a square root is an odd number too. √16 = 4. Here 16 is an even number and the square root of an even number is always even.
  • Property 4: We cannot use the square root of a negative number since it is an irrational number. For example, √-6 is not possible since it is an irrational number or rather a complex number.
  • Property 5: The total sum of first n odd numbers calculates to n^2. For example: 1 + 3 + 5 +7 = 16. Here there are 4 odd numbers. Thus following the equation it represents n^2 = 4^2 = 16.

These are a few basic properties and characteristics of square roots. To get a better insight into the concept regarding square root and cube root, do check with our teachers and lessons found online at Cuemath.

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