36 = 6 9 × 4 = 3 × 2 = 6 36 = 9 × 4 81 = _____ 9 × 9 = _____ × _____ = _____ 81 = 9 × 9

Given: 36 = 6 ........(i) 9 × 4 = 3 × 2 = 6 ......(ii) We have 36 = 6 9 × 4 = 6 Hence, 36 is equal to 9 × 4 Now, 81 = 9 2 = 9 .......(iii) 9 × 9 = 3 × 3 = 9 .....(iv) From (iii) and (iv) we get, 81 = 9 × 9

144 = _ _ _ _ 9 × 16 = _ _ _ _ × _ _ _ _ = _ _ _ _ 144 = 9 × 16 144 = _ _ _ _ 36 × 4 = _ _ _ _ × _ _ _ _ = _ _ _ _ 144 = 36 × 4

Given: 144 = _ _ _ _ ........(i) 9 × 16 = _ _ _ _ × _ _ _ _ = _ _ _ _ ......(ii) We have 144 = 12 9 × 16 = 3 × 4 = 12 Hence, 144 is equal to 9 × 16 Now, 144 = 12 2 = 12 .......(iii) 36 × 4 = 6 × 2 = 12 .....(iv) From (iii) and (iv) we get, 144 = 36 × 4

100 = _ _ _ _ 25 × 4 = _ _ _ _ × _ _ _ _ = _ _ _ _ 100 = 25 × 4 1225 = _ _ _ _ 25 × 49 = _ _ _ _ × _ _ _ _ = _ _ _ _ 1225 = 25 × 49

Given: 100 = _ _ _ _ ........(i) 25 × 4 = _ _ _ _ × _ _ _ _ = _ _ _ _ ......(ii) We have 100 = 10 25 × 4 = 5 × 2 = 10 Hence, 100 is equal to 25 × 4 Now, 1225 = 35 2 = 35 .......(iii) 25 × 49 = 5 × 7 = 35 .....(iv) From (iii) and (iv) we get, 1225 = 25 × 49

Put the numbers 4 , 14 , 5 in ascending order.

To put the numbers 4 , 14 , 5 in ascending order, We know that 14 is not a square number. However, we can estimate an approximation to 14 and use it here. Squaring the numbers 4 , 14 , 5 , we get 16 , 14 , 25 respectively. Thus, in ascending order 14 < 16 < 25 which can be written as 14 < 4 2 < 5 2 . Considering the square root, we have 14 < 4 < 5 . Hence, ascending order of above numbers are 14 < 4 < 5 .

Put the numbers 7 , 65 , 8 in ascending order.

To put the numbers 7 , 65 , 8 in ascending order, We know that 65 is not a square number. However, we can estimate an approximation to 65 and use it here. Squaring the numbers 7 , 65 , 8 , we get 49 , 65 , 64 respectively. Thus, in ascending order 49 < 64 < 65 which can be written as 7 2 < 8 2 < 65 . Considering the square root, we have 7 < 8 < 65 . Hence, ascending order of the numbers are 7 < 8 < 65 .