NCERT Solutions for Class 8 Maths Chapter 1

                                                           

NCERT Solutions for Class 8 Maths Chapter No. 1 

Square and Cube EXERCISE 1.1

• Chapter No. 1      SQUARE AND CUBES

INTRODUCTION

1.    If "n" is a number, then n × n or n² will be known as its square and n × n × n or  n³ will be called its 

        cube.

2.     Those numbers whose unit place have numbers like 2, 3, 4, or 8 cannot be perfect square numbers.

3.     If  a perfect square number ends in an even number of zeroes, then they would also be perfect squares.

4.    The squares and cubes of even numbers are always  even numbers and squares and cubes of odd 

        numbers are always odd numbers.

5.    The squares of any natural number "n" is the sum of the initial consecutive odd numbers.

6.     If three numbers are in such a sequence that the square of the greater number is equal t the sum of the         square of the remaining two numbers, then the numbers are known as Pythagoral Triplets e.g.   3² + 4² =  5²   therefore (3, 4, 5) make a Pythagoral Triplet.

7.      Square root is represented b the symbol "  √  ".  This is known as the symbol of under root or the

         square  root of the number. The number written under this symbol is determined.

                                              Exercise 1.1

Q.1. Pairs the multiple factors of the following number and say whether they are perfect squares or                not?
(1)      164
Sol:-

(2)     121

Sol:-

(3)      289

Sol:-   

          289 = 17*17

(4)     729

Sol:-

      

(5)     1100

Sol:-

Q.2.   Give reasons why the given numbers are not perfect squares.

(1)     12000

Sol:-  A perfect square never has odd number of zero in the end of the number, so 12000 is not a                    perfect square.

(2)     1227

Sol:-  The units digit of a perfect square is never 2, 3, 7 or 8, so 1227 is not a perfect square.

(3)     790

Sol:-  A perfect square never has odd number of zero in the end of the number, so 790 is not a                    perfect square.

(4)     1482

Sol:-  The unit digit of a perfect square is never 2, 3, 7 or 8, so 1482 is not a perfect square.

(5)     165000

Sol:-  A perfect square never has odd number of zero in the end of the number, so 165000 is not a                  perfect square.

(6)     15050

Sol:-   A perfect square never has odd number of zero in the end of the number, so 15050  is not a                  perfect square.

(7)     1078

Sol:-  The unit digit of a perfect square is never 2, 3, 7 or 8, so 1078  is not a  perfect square.

(8)     8123

Sol:-   The unit digit of a perfect square is never 2, 3, 7 or 8, so 8123  is not a  perfect square.

Q.3.   Find out the numbers whose squares are even numbers and whose squares are odd numbers?

Sol:- Since the square of even numbers are always even and square of odd number are always odd,               so  square of 14, 608, 11288, and 4010 are even numbers and square of 277, 179, 205, 1079,               1225, are odd numbers.

Q.4.   Look at the given pattern and fill in the blanks:-

                     

Sol:-      

                          

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Exercise 1.2

Q.1.   Identify the perfect cubes in the given numbers.

(1)     125

Sol:-

125 is perfect cube.    Ans.

(2)     800
Sol:-

800 = 2*2*2*2*2*5*5

800 is not a perfect cube.      Ans.

(3)     729

Sol:-   

729 = 3*3*3*3*3*3


729 is a perfect cube.      Ans.


(4)      2744
Sol:-







2744 = 2*2*2*7*7*7



2744 is a perfect cube.       Ans.

(5)       22000
Sol:-








22000 = 2*2*2*2*5*5*5*11


22000 is not a perfect cube.    Ans.

(6)      832
Sol:-










     832 is not a perfect cube.    Ans.



Q.2.   Find out that smallest number which when multiplied by 256 will make the product a                  perfect cube.
Sol:-  Prime factors of 256.
       





256 = 2*2*2*2*2*2*2*2

Here, we get 2 triples of prime factors 2 but to get a third triple we will have to multiply once by 2.

 So, the given number should be multiplied by 2 to get a perfect cube.    Ans.



Q.3.   Find out the smallest number which when multiplied by 1352 will make the product a                  perfect cube.
Sol:-  Prime factor of 1352




Here in the factors of 1352, we get the triple of 2  but we do not get a triple of 13. So 1352 should be multiplied by 13. So that it become a perfect cube.                      Ans. 





Q.4.    Find out that smallest number which when multiplied by 8019 will make the quotient a                perfect  cube.
Sol:-   Prime factor of  8019
           





8019 = 3*3*3*3*3*3*11

Here in the factors of 8019, we get 2 triple of 3 but do not get a triple of  11 so that it becomes a perfect cube.             Ans.

For more help visit : https://www.learncbse.in/ncert-solutions-for-class-8-maths/ 

Exercise 1.3

Q.1.     Find out the square root of the given numbers by prime factorization method.

(1)       361

Sol:-

Ans.

(2)       400

Sol:- 

Ans.

(3)      784

Sol:-  

Ans.

(4)      1024

Sol:- 

Ans.

(5)      2304

Sol:-

Ans.

(6)       7056

Sol:-

Ans.

Q.2.      A group of boys bought 256 mangoes and distributed it among themselves. If each boy                 got the number of mangoes equal to the number of boys in the group. Find out the                       number of boys in the group.

Sol:-     Let the number of boys in each group be x then each of x boys gets x mangoes.

             So total mangoes = x*x = x² 

             But total number of mangoes = 256

             So,      x²     = 256  

                                X² =2  × 2 × 2 × 2 × 2  × 2 × 2 × 2

              Taking square rot of the both sides

                √ x²=√2  × 2 × 2 × 2 × 2  × 2 × 2 × 2        (all numbers are in square rooot)

                   x =  2  × 2 × 2 × 2

                   x = 16

             So, the number of boys in each group are 16.          Ans.




For more help visit : https://www.learncbse.in/ncert-solutions-for-class-8-maths/ 

Exercise 1.4

Q.1.    Find out the square root of following by division method.

(1)     529
Sol:-







23 is Ans.

(2)       1369
Sol:-







 37 is Ans.

(3)      1024
Sol:-

32 is Ans.


(4)      5776
Sol:-






76 is Ans.


(5)      900
Sol:-






30 is Ans.
(6)       7921
Sol:-

0 is Ans.

(7)        50625
Sol:-

225 is Ans.

(8)       363609
Sol:-











6703 is Ans.

Q.2.     In a cinema hall the owner wants to organize the chair in this way that the number of 

            rows and columns of seats should be equal. If there are total 1849 seats then find out the 

            numbers of rows and column.

Sol:-    Given that,

                              the total number of seats are 1849

                               Then, the number of columns and rows are

                                   1849 = 43*43

                       hence the number of rows and columns are 43              Ans.

Q.3.      The area of a square garden is 1444 square meter, so find out the length and breadth of 

             that garden.

Sol:-      Given that, 

                             the area of a square garden is 1444 sq.m.

                            then, the length and breadth of that garden will be

             we know that area of square is = L× L

                      so the length of the garden well be 

                                      1444 = 38 × 38             

                   Hence, the length and breadth of the garden is same 38 m.          Ans.

For more help visit : https://www.learncbse.in/ncert-solutions-for-class-8-maths/ 

  Exercise 1.5

Q.1.       Find out the squares root of following numbers.

(1).        7.29

Sol:-        

Ans.

(2).       16.81
Sol:-








Ans.

(3).       9.3025
Sol:-










Ans.


Q.2.      Find out the squares root of following up to two places of decimal.

(1).     0.9
Sol:-










Ans.

(2).     5
Sol:-










Ans.

(3).     7
Sol:-










Ans.



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Exercise 1.6

Determine the cube root of following.

(1).    125

Sol:-  

Ans.


(2)     343
Sol:-











Ans.

(3).     1331
Sol:-









Ans.



(5).     9261
Sol:-












Ans.

(6)    166375
Sol:-











Ans.

(7)      4913
Sol:-










Ans.

(8)     42875
Sol:-












Ans.



For more help visit : https://www.learncbse.in/ncert-solutions-for-class-8-maths/ 

WE HAVE LEARNT

1.    If "n" is a number, then n × n or n² will be known as its square and n × n × n or  n³ will be called its 

        cube.

2.     Those numbers whose unit place have numbers like 2, 3, 4, or 8 cannot be perfect square numbers.

3.     If  a perfect square number ends in an even number of zeroes, then they would also be perfect squares.

4.    The squares and cubes of even numbers are always  even numbers and squares and cubes of odd 

        numbers are always odd numbers.

5.    The squares of any natural number "n" is the sum of the initial consecutive odd numbers.

6.     If three numbers are in such a sequence that the square of the greater number is equal t the sum of the          square of the remaining two numbers, then the numbers are known as Pythagoral Triplets e.g.                             3² + 4² = 5²   therefore (3, 4, 5) make a Pythagoral Triplet.

7.      Square root is represented b the symbol "  √  ".  This is known as the symbol of under root or the

         square  root of the number. The number written under this symbol is determined.