NCERT Solutions Class 8 Maths Ganita Prakash Chapter 1 A Square and A Cube on Padhaiwise

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 1 A Square and A Cube Figure it Out Page 10

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 1 — Figure it Out (Page 10)#

A perfect square is a number of the form $n \times n$. A perfect square always ends in 0, 1, 4, 5, 6 or 9, and its prime factors can be split into two identical groups. These two facts solve most of the questions below.

1. Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089 #

Solution

A perfect square can only end in 0, 1, 4, 5, 6 or 9. We look at the last digit of each number:

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 1 A Square and A Cube Figure it Out Page 16

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 1 — Figure it Out (Page 16)#

A perfect cube is a number of the form $n \times n \times n$. Its prime factors can be split into three identical groups, and its cube root is the product of one group. The last digit of a cube also tells us the last digit of its cube root.

1. Find the cube roots of 27000 and 10648. #

Solution

Cube root of 27000. We write 27000 as $27 \times 1000$ and factorise: