Consider the square root of 64 i.e. Ö64. Now to find it, you have to find a number when multiplied by itself gives you 64. The square root of 64, then it is 8. Ö is the symbol for the square root. Now the natural question comes into your mind, what is the sign of a square root. The answer is very simple, it depends upon the requirement of the problem. Therefore, Ö100 = 10 and - Ö144 = -12 etc.

To find the cube root of a number, you want to find a number that when multiplied by itself two times, gives you the original number. For example to find cube root of 27, you want to find the number that when multiplied by itself twice gives you 27 i.e. 3 ´ 3 ´ 3 = 27.

Note that the symbol for square root is Ö and for cube root is the radical sign with a small three ( the index ) i.e.

SOME perfect square roots ( of whole numbers )

SOME perfect cube roots ( of whole numbers )

Square roots by factors

(1) Find prime factors of the given numbers

(2) Arrange the factors in pairs

(3) Take one factor from each pair

(4) Find the product of these factors, which gives the square root of the given number.

Example Find the square root of 3249

Solution : To find the prime factors of 3249, we shall use successive division method:

\ 3249 = 3 ´ 3 ´ 19 ´ 19

= 3² ´ 19²

\ Ö3249 = 3 ´ 19

= 57

Check : 57 ´ 57 = 3249

Square root using tables

STEPS

(1) Put the given number in the form A ´ 10ⁿ , where A is any rational

number and ’ n ’ is any even integer.

(2) In this rational number, if one figure is left before the decimal point, use

the upper line of a pair, if it leaves two figures before decimal point, use

the lower line.

(3) Insert the decimal point by inspection.

Example Evaluate use the result to find

Solution : 777.35 = 7.7735 ´ 10²

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Index

Introduction
1.1 Pre-requisties
1.2 Common Mathematical Symbols
1.3 Some Properties of Basic Mathematical Operations
1.4 Real Numbers

Chapter 2