fill in the blanks the value of a is. ,b is and the square roots 361 IS 19
Answers
SOLUTION
TO DETERMINE
To fill in the blanks :
(а) The perfect square number between 60 and 70 is ______
(b) The square root of 361 ends with digit ______
EVALUATION
ANSWER TO QUESTION : (a)
We have
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
Hence we can conclude that :
The perfect square number between 60 and 70 is 64
ANSWER TO QUESTION : (b)
Here the given number is 361
We now prime factorise the given number
361 = 19 × 19 = 19²
Thus we get
Now unit digit of 19 = 9
Hence we can conclude that :
The square root of 361 ends with digit 9
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Complete Question :- fill in the blanks :-
(а) The perfect square number between 60 and 70 is ______ ?
(b) The square root of 361 ends with digit ______ ?
Solution :-
(a)
we know that, perfect square upto 100 are :-
→ 1² = 1
→ 2² = 4
→ 3² = 9
→ 4² = 16
→ 5² = 25
→ 6² = 36
→ 7² = 49
→ 8² = 64
→ 9² = 81
→ 10² = 100
as we can see that, 64 is the perfect square of number 8 that lies between 60 and 70 .
→ 60 < 64 < 70
therefore, the perfect square number between 60 and 70 is 64 .
(b) Basic Method :-
→ √(361)
→ √(19 * 19)
→ √(19)²
using √(a²) = a ,
→ 19
therefore, The square root of 361 ends with digit 9 .
Conceptual Method :-
concept for unit digit of a square number :-
→ 1² = 1 = unit digit 1 .
→ 2² = 4 = unit digit 4.
→ 3² = 9 = unit digit 9.
→ 4² = 16 = unit digit 6.
→ 5² = 25 = unit digit 5.
→ 6² = 36 = unit digit 6 .
→ 7² = 49 = unit digit 9.
→ 8² = 64 = unit digit 4.
→ 9² = 81 = unit digit 1.
→ 10² = 100 = unit digit 0.
So, unit digit of a square number is depends on the unit digit of square root of that number..
Conclusion :-
- unit digit 1 in last = 1 or 9.
- unit digit 4 in last = 2 or 8.
- unit digit 6 in last = 4 or 6.
- unit digit 9 in last = 3 or 7.
- unit digit 5 in last = 5
- unit digit 0 in last = 0 .
now, given number is 361
→ 361 = unit digit 1 in last = square root has 1 or 9 in last .
now,
→ 3(61) = Last two digits are to find unit digit of square root only .
now, as we can see that, left digit is 3 and upto 3 we can go to square of 1 as 1² = 1 .
then, we can conclude that, 361 is either square of 11 or 19 .
checking,
→ 11² = 11 * 11 = 121
→ 19² = 19 * 19 = 361
therefore, we can conclude that, square root of 361 is 19 .
Hence, The square root of 361 ends with digit 9 .
Note :- This method will help us in finding unit digit or square root of greater values .
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