Question

Write the possible units digits of the square roots of the following numbers. Which of these number have odd square roots?
(i) 9801
(iii) 998001
(11) 99856
(iv) 65766602​

Answer 1

Answer:

Step-by-step explanation:

i. We know that the unit’s digit of the square of a number having digit as unit’s place 1 is 1 and also 9 is 1[9^{2}9  

2

 =81 whose unit place is 1].

∴ Unit’s digit of the square root of number 9801 is equal to 1 or 9.

ii. We know that the unit’s digit of the square of a number having digit as unit’s place 6 is 6 and also 4 is 6 [6^{2}=36 \text { and } 4^{2}=166  

2

=36 and 4  

2

=16, both the squares have unit digit 6].

∴ Unit’s digit of the square root of number 99856 is equal to 6.

iii. We know that the unit’s digit of the square of a number having digit as unit’s place 1 is 1 and also 9 is 1[9^{2}9  

2

 =81 whose unit place is 1].

∴ Unit’s digit of the square root of number 998001 is equal to 1 or 9.

iv. We know that the unit’s digit of the square of a number having digit as unit’s place 5 is 5.

∴ Unit’s digit of the square root of number 657666025 is equal to 5.

ANSWERED BY GAUTHMATH

Answer 2

Answer:

4) 65766602 is the answer