Question

33. Square of which of the following number
will have 6 at its unit place?
(A) 38 (B) 24
(C) 32 (D) 45
34. How many natural numbers exist between
the squares of 28 and 29?
(A) 30 (B) 58
(C) 56 (D) 60​

Answer 1

Answer:

1.B.24

2.the answer is 57

Answer 2

33. Square of which of the following number  will have 6 at its unit place?

we use the formula: (a - b)² = a² + b² - 2ab

(a + b)² = a² + b² + 2ab

(A) 38

= 40 - 2

38² = (40 - 2)²

= 40² + 2² - 2 × 40 × 2

= 1600 + 4 - 160

= 1444

(B) 24

= 20 + 4

24² = (20 + 4)²

= 20² + 4² + 2 × 20 × 4

= 4000 + 16 + 160

= 576

(C) 32

= 30 + 2

32² = (30 + 2)²

= 30² + 2² + 2 × 30 × 2

= 9000 + 4 + 120

= 1024

(D) 45

= 40 + 5

45² = (40 + 5)²

= 40² + 5² + 2 × 40 × 5

= 1600 + 25 + 400

= 2025

Therefore option (B) 24 is correct.

34. How many natural numbers exist between  the squares of 28 and 29?

we use the formula: a² - b² = (a + b) (a - b)

The natural numbers between 28² and 29² are:

= 28² - 29² - 1

= [ (28 + 29) × (28 - 29) ] - 1

= (57) (1) -  1

= 57 - 1

= 56

Therefore, 56 natural numbers exist between  the squares of 28 and 29