How many four - digit perfect square number have 4 ; 5 or 6 in their units place ?
Answers
Step-by-step explanation:
In case of 4-digit perfect squares,
Smallest =1024=322
Largest =9801=992
=> There are (99−32+1)=68 4-digit perfect squares.
Now, we have to find how many of them have 4 , 5 and 6 in their units place.
Case 1: 4 in Units place
Rule: If a number has 2 or 8 in the unit place, then its square has 4 in the units place
So, going by this logic, the possibilities are 32² , 38² , 42² , 48² , 52² , 58²,…., 92² and 98²
So, 14 such numbers
Case 2: 5 in units place
Rule: If a number has 5 in the unit place, then its square has 5 in the units place
Going by this logic, the possibilities are 35² , 45², 55² , …., 85²
So, 7 such numbers
Case 2: 6 in units place
Rule: If a number has 4 or 6 in the unit place, then its square has 6 in the units place
Case 2: 6 in units place
Rule: If a number has 4 or 6 in the unit place, then its square has 6 in the units place
Going by this logic, the possibilities are 34² , 36² , 44², 46² , 56² , …., 94² , 96²
So, 14 such numbers
TOTAL = 14 + 7 + 14 = 35
Thus, 35 such 4-digit number are there. (Answer)
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