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Find the square root of the following

using square root tables:

a). 0.83

b). 0.03857

c). 0.6

d). 0.0067

 

Lesson Objectives

By the end of the lesson you should be able to;

find square root of positive numbers using the mathematical 

tables correctly.

INTRODUCTION

Find the square root of the following by factorisation.

a). 25

b). 48

Solution

a). 25 = 5 x 5 Therefore 25 = 5

25 is a perfect square


b). 48 = 24 x 3 = 2 x 2 x 2 x 2 x 3

We notice that it is not possible to group the factors

into two equal groups the factors into two equal groups

hence it is not possible to get square root of 48 by

factorisation.

Another methods of finding square root is by the use of square root tables

Square root tables give the square root of numbers

from 1 to 100 directly. The square root tables have three

sections similar to those of the square tables and they are

used in a similar manner.


Find the square root of

a). 16


b). 25

a). 16 This is written as 16.0

Under column marked x, locate 1 From 16, move

horizontally to value under the column marked .0,

the value is 4.000 which is the square root of 16.6

Activity 1


Use the square root tables to find the square root of 49

The square root of 49 is 7.000

Case 2

Find the square root of


a). 34


b). 58


c). 67


Solution

a). 34 written as 34.0

Under column x locate 34; move horizontally to value

under colum 0 the value is 5.831


Therefore 58 = 5.831

b). 58 written as 58.0

Under colum x locate 58. 

Move horizontally to the value under column 0, the is 7.616.


Therefore 58 = 7.616


c). 67 Written as 67.0

Under column x locate 67; move horizontally to the

value under column 0, the value is 8.185


Therefore = 8.185 

Activity


Using square root tables find the square root of


a). 7


b). 84

Solutions

2 = 2.646

84 = 9.165

Case 3

Find the square toor of the following using square

root tables:

a). 1.25


b). 10.36


c). 45.67


d). 6


a). 1.25 under column x locate 1.2; more horizontally

to the value under columns the value is 1.118


Therefore 1.25 = 1.118

b). 10.36


Under column x locate 10, move horizontally to

the value under 3, the value is 3.209, Move further

horizontally to the extension under column 6 to get 9


Ad 9 to the decimal part 209 to get 218.


The square root of 10.36 therefore 3.218.

c). 45.67

Under column x locate 45, move horizontally to the

value under 6, the value is 6.753, move further

horizontally to the extension under column 7 to get 5.


Add 5 to the decimal part which 753 to get 758.

Therefore the square root 45.67 is 6.758

d). 16 1/4

Convert 16 1/4 to a decimal 16.25

Locate 16 under column x, move horizontally to

Column under 2, the value 4.025, move further horizontally

to the extension under column 5 to get 6, add 6 to the decimal

part to get 031 therefore, the square root of is 4.031


Case 4

Find the square root of the following using square root tables:

a). 120

b). 235.2

To find the square root of numbers more than 100 using square root tables

i). Write the number in the form Ax10n

Where A is between 1 and 100 and n is an even number

ii). The squarere root will be x Where = 10n-2

10n-2 where the number of steps the decimal point moves to

the right


2. To find the square root of numbers less that 1 using the

square of numbers less that 1 using the square root tables.

ii). Write the number in the form Ax 10-n


iii). The square root will be x

n-2 means the number of steps the decimal pont moves to the left

Solution

The square root 120 is the square root of 1.2 times the square root of 102


That is = 120 = 1.095 x 10 = 10.95

b). 2356.7

This is written as 23.567 x 102

The square root will be square root of 23.567 times the square root of 102

That is 23.567 is rounded off to be 23.57


Therefore 23.567 is rounded off to be 23.57.


23.567 = 4.848 add 7

That is 4.848

+ 7

SQUARE ROOTS

Square roots can be found using differnt ways . Some these ways are using prime factorisation, estimating and square root table.

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