Question

square of which of the following number will have 6 at its unit place?


a) 38
b)24
c)32
d)45

exaplain me how... please..​

Answer 1

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

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

(a + b)? = a? + b² + 2ab =

(A) 38

= 40 - 2

38? = (40 - 2)?

= 402 + 22 - 2 x 40 x 2

= 1600 + 4 - 160

= 1444

(B) 24

= 20 + 4

242 = (20 + 4)

= 202 + 4? + 2 × 20 x 4 =

= 4000 + 16 + 160

= 576

(C) 32

= 30 + 2

322 = (30 + 2)?

= 302 + 22 +2 x 30 x 2

= 9000 + 4 + 120

1024

(D) 45

= 40 + 5

452 = (40 + 5)2

= 402 + 52 + 2 x 40 x 5

= 1600 + 25 + 400

= 2025

5. Shuja-ud-din cheril

Therefore option (B) 24 is correct.

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

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

The natural numbers between 282 and 29 are:

= 282 - 292 - 1

= [ (28 + 29) x (28 - 29) ] - 1

= (57) (1) - 1

= 57 - 1

= 56

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