Can there be a perfect square whose digits consist of exactly 4 ones 4 twos and 4 zeros in any order?
Can there be a perfect square whose digits consist of exactly 4 ones 4 twos and 4 zeros in any order?
No , there cannot be a perfect square. The number is divisible by 3.
What is the smallest 4 digit perfect square number?
So, the smallest four digit number which is a perfect square must be near to 1000. Hence, The smallest four digit number which is a perfect square is 1024.
How many three digit numbers exist such that middle digit is a smallest of 3 digits?
The largest 4 digit number is 9,999. The smallest positive 3 digit number is 100. But “smallest” can include negative numbers. The smallest 3 digit number is -999.
How many three digit integers are there in which the first digit from left is greater than the second digit and the second digit is greater than the third digit?
The answer is 285. List all the three-digit integers in r where the first digit is greater than the second or third digit.
How many perfect 4-digit square root numbers are there?
The only numbers in the list that are the “reverse” of another are 1089 and 9801. Since ( d c b a) 10 must be a factor of ( a b c d) 10 and not the other way around, the only solution is ( a b c d) 10 = 9801. Thus, there is exactly 1 such perfect 4-digit square.
How many perfect square numbers are there after 1000?
The first number which is a perfect square after 1000 is 1024 = 32 square. The last number which is a perfect square before 9999 is 9801 = 99 square. 99 -32 +1 = 68 numbers.
What are the 4-digit perfect squares that are multiples of 11?
The 4-digit perfect squares that are multiples of 11 are: 33 2 = 1089, 44 2 = 1936, 55 2 = 3025, 66 2 = 4356, 77 2 = 5929, 88 2 = 7744, 99 2 = 9801. The only numbers in the list that are the “reverse” of another are 1089 and 9801. Note that ( a b c d) 10 + ( d c b a) 10 = 1001 ( a + d) + 110 ( b + c) ≡ 0 ( mod 11).
What is the unit digit of a perfect square?
The unit digit of a perfect square is the unit digit of the square of the square root of the perfect square, so let us look at the squares of all single digits: Therefore, squares of any number with unit digit 4 or 6 have digit 6 in the unit’s place.