Students can Download Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.6 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.
Karnataka Board Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.6
Question 1.
Looking at the pattern fill in the gaps in the followings.
Answer:
| 2 | 3 | 4 | -5 | 6 | 8 | -9 |
| 23= 8 | 33 = 27 | 43 = 64 | -53 = -125 | 63 = 216 | 83 = 512 | -93 = -729 |
Question 2.
Find the cubes of the first five odd natural numbers and the cubes of the first five even natural numbers. What can you say about, the parity of the odd cubes and even cubes?
Answer:
13 = 1 × 1 × 1 = 1
23 = 2 × 2 × 2 = 8
33 = 3 × 3 × 3 = 27
43 = 4 × 4 × 4 = 64
53 = 5 × 5 × 5=125
63 = 6 × 6 × 6 = 216
73 = 7 × 7 × 7 = 343
83 = 8 × 8 × 8 = 512
93 = 9 × 9 × 9 = 729
103 = 10 × 10 × 10 = 1000
The cube of an odd number is odd and the cube of an even number is even.
Question 3.
How many perfect cubes you can find from I to 100? How many from -100 to 100?
Answer:
From 1 to 100 there are 4 perfect cubes. 1, 8, 27, 64 From -100 to 100 there are 9 perfect cubes -64, -27, -8, -1, 0, 1, 8, 27, 64
Question 4.
How many perfect cubes are there from 1 to 500? How many are the perfect square among these cubes?
Answer:
From 1 to 500 there are 7 perfect cubes and 2 of these are perfect squares.
Perfect cubes 1, 8, 27, 64, 125, 216, 343,
Perfect squares are 1 = 12 = 13 and 64 = 82 = 43
Question 5.
Find the cubes of 10, 30, 100, 1000. What can you say about the zeros at the end?
Answer:
103= 10 x 10 x 10 = 1.000 (3 zeros)
303 = 30 × 30 × 30 = 27000 (3 zeros)
1003 = 100 × 100 × 100 = 1000000 (6 zeros)
10003 = 1000 × 1000 × 1000 = 1000000000 (9 zeros)
The number of zeros at the end are always multiple of 3.
Question 6.
What are the digits in the units place of the cubes of 1,2,3,4,5,6,7,8,9,10? Is impossible to say that a number is not a perfect cube by looking at the digit in the units place of the given number, just like you did for squares?
Answer:
13=1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
103 = 1000
∴ It is not possible to say whether the number is a perfect cube (or) not looking at the digit in unit place.