Chapter 1: Square and Square Roots

The square of the number  means product of that number with itself two times.

For example : 1) The square of 2 = 2 x 2 = 4.

                      2) The square of 3 = 3 x 3 = 9.

 Always remember the squares of the following numbers 1 to 30.

   

Example : 1) The square of (-6) is (-6) x (-6) = 36.

                2) The square of (-10) is (-10) x (-10) = 100.

 

---

The square of the negative number is always positive.

Example : 1) The square root of 36 are (-6) and 6.

                2) The square of 100 are (-10) and 10.

---

Writing and reading a square root :

 

A square root is written using the sign '\/^---'

Example : 1) \/49 means positive square root of 49.

            2) -\/49 means negative square root of 49.

---

Perfect Square : A number which is the square of an integer is called a perfect square.

Example : 4, 9, 16, 25, 36, 49, 64 are perfect squares. But the numbers 2, 3, 5, 7, 11, 13, 14, 15 are not perfect squares.

   

---

The square root of the number 289 by division method 

 

The square root of non perfect square number 20:

• \/20 = 4.4721.... (The dots on right denote that further there will be infinite number of digits.
• 
  
  
  

  ---

  The square root of 20 up to two decimal places is 4.47
  The square root of 20 up to three decimal places is 4.472
  The square root of 20 up to four decimal places is 4.4721

  The square root of a decimal fraction by division method :  

  Exercise : Find the square root of 555.5449 by division method.
   
  Examples: 1) \/56.25 = 7.5
                   2) \/151.29 = 12.3
                   3) \/49.5616 = 7.04
                   4) \/3.4158 = 1.85
                   5) \/720.5 = 26.84
  

  ---

  Pythagoras theorem : (Hypotenuse)²=(Base)²+(Height)²

  In ABC, AB = 4 cm, BC = 2 cm, m<B = 90⁰,
  Then by Pythagoras Theorem,
  
  AC² = AB² + BC² =
          =2²+4² = 4 + 16 = 20      
  
  AC = \/20
  Hence the length of seg AC is equal to the square root of 20.