173
32,768
The largest 3-digit number - not itself a perfect square - is 999. Calculate its square root, round the answer down, then square the answer again.
To simplify 64, we need to find the largest perfect square that divides evenly into 64. In this case, the largest perfect square that divides evenly into 64 is 64 itself. Therefore, the simplified form of 64 is 64.
Think of the largest number you can. Then square it. Then square that one. Since numbers don't stop, squares don't stop either.
The smallest integer is 11 but there is no smallest number! 0.11 is a smaller number and will give a perfect square. 0.0011 is smaller still, and 0.000011 even smaller. That sequence is endless!
32,768
4
The largest two-digit number with exactly three factors is 99. A number has exactly three factors if it is the square of a prime number, specifically in the form ( p^2 ) where ( p ) is a prime. The only prime number whose square is a two-digit number is 7, since ( 7^2 = 49 ) and ( 11^2 = 121 ) exceeds two digits. Thus, 49 is the largest two-digit number with exactly three factors.
25
81 is the largest square of a whole number...
9
Yes, there is. Just as there is no largest number, there is no largest square number. For example, if you calculate the square of 975, you get a number that is (a) larger than 975, and (b) by definition, a square number.
456788
The largest two-digit number that has exactly three factors is 99. A number has exactly three factors if it is the square of a prime number. In this case, ( 9 = 3^2 ) has three factors: 1, 3, and 9. However, since 99 is the largest two-digit number, we consider its factors, but it does not meet the criterion. The correct answer is 81, which is ( 9^2 ).
The largest 3-digit number - not itself a perfect square - is 999. Calculate its square root, round the answer down, then square the answer again.
To simplify 64, we need to find the largest perfect square that divides evenly into 64. In this case, the largest perfect square that divides evenly into 64 is 64 itself. Therefore, the simplified form of 64 is 64.
To find the largest perfect square that divides 4312 without a remainder, we first perform its prime factorization. The prime factorization of 4312 is (2^3 \times 7 \times 154), which further factors into (2^3 \times 7 \times 2 \times 77 = 2^4 \times 7^1 \times 11^1). The largest perfect square must use the highest even powers of the prime factors: (2^4) (which is 16) and (7^0) (which is 1). Therefore, the largest perfect square that divides 4312 is (16).