Describe Solving Square Roots


The square root of any number is equal to a number, which when squared gives the original number.

Let us consider p is a positive integer then,

⇒ √(p×p)

⇒ √p2

⇒ p

The square of any number can be calculated by multiplying the number with itself.

Properties of  Square Roots

  • A perfect square root occurs when a number is a perfect square number.
  • A square root can be found if a number has an even number of zeros.
  • It is possible to multiply the two square root values. For instance, if you multiply√2 by √3, the result should be√6.
  • The product of multiplying two identical square roots should be a radical number. It indicates that the answer is non a square root number. If√3 is multiplied by√3,  the answer is 3.
  • The square root of any negative numbers is not defined. Because the perfect square cannot be negative.
  • The perfect square root does not exist if a number ends in 2, 3, 7, or 8 (in the unit digit).
  • If the unit digit of a number ends in 1, 4, 5, 6, or 9, the number does have a square root.

How do Find Square Root?

  • To determine square the square root, we must first determine if it is a perfect square or an imperfect square.
  • If the number is a perfect square, such as 4, 9, 16, etc., we can use the prime factorization method to factorize it.
  • We must use the long division method to find the root if the number is an imperfect square, such as 2, 3, 5, and so on.


Square of 7 = 7 x 7 = 72 = 49
The square root of 49 is,

49 = 7

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