Q2 of 67 Page 86

Express 144 as a sum of 12 odd numbers.

As we know, that sum of first n odd natural numbers is n²

Sum of above digits = 144

⇒ Number of digits = √144

= 12

So, digits are 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Find numbers from 100 to 400 that end with 0, 1, 4, 5, 6 or 9, which are perfect squares.

Find the sum 1 + 3 + 5 + … + 51 (the sum of all odd numbers from 1 to 51) without actually adding them.

Find the 14^th and 15^th triangular numbers, and find their sum. Verify the Statement 8 for this sum.

What are the remainders of a perfect square when divided by 5?

Questions · 67

5. Squares, Square-Roots, Cubes and Cube-Roots

1 2 3 4 5 1 2 3 4 1 1 1 1 2 3 1 1 1 1 1 2 2 2 2 2 2 3 4 5 1 2 3 1 2 3 4 5 6 1 1 1 1 1 2 2 2 3 1 2 2 2 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16