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What is the smallest perfect square that is divisible by the four smallest prime numbers?
44,100
What is the smallest positive integer n such that 2n is a perfect square 3n is a perfect cube and 4n is a perfect fourth?
To find the smallest positive integer ( n ) such that ( 2n ) is a perfect square, ( 3n ) is a perfect cube, and ( 4n ) is a perfect fourth, we analyze the conditions for each case using prime factorization. Let ( n = 2^a \cdot 3^b \cdot k ), where ( k ) is coprime to 2 and 3. For ( 2n ) to be a perfect square, ( a+1 ) must be even and ( b ) must be even. For ( 3n ) to be a perfect cube, ( a ) must be divisible by 3 and ( b+1 ) must be divisible by 3. For ( 4n ) to be a perfect fourth, ( a+2 ) must be divisible by 4 and ( b ) must be divisible by 4. By solving these conditions simultaneously, the smallest ( n ) that meets all conditions is ( n = 108 ).
What is the smallest positive integer value of x for which 54x is a perfect square?
324
What is the smallest positive whole number that 150 can be multiplied by to make a perfect square.?
How about 150*6 = 900 which is a perfect square because 30*30 = 900
What are the characteristics of a perfect square?
divisible by 2
What is the smallest positive perfect square that is divisible by the four smallest prime numbers?
(3x5x7x11)2 =1334025
What is the smallest perfect square that is divisible by the four smallest primes?
44,100
Smallest perfect square divisible by 7?
It is 49.
What is the smallest perfect square that is divisible by the four smallest prime numbers?
44,100
What is the smallest positive integer that has exactly 6 perfect square divisors?
the answer is 144, it is divisible by 1, 4, 9, 16, 36, and 144.
What is the smallest positive integer n such that 2n is a perfect square 3n is a perfect cube and 4n is a perfect fourth?
To find the smallest positive integer ( n ) such that ( 2n ) is a perfect square, ( 3n ) is a perfect cube, and ( 4n ) is a perfect fourth, we analyze the conditions for each case using prime factorization. Let ( n = 2^a \cdot 3^b \cdot k ), where ( k ) is coprime to 2 and 3. For ( 2n ) to be a perfect square, ( a+1 ) must be even and ( b ) must be even. For ( 3n ) to be a perfect cube, ( a ) must be divisible by 3 and ( b+1 ) must be divisible by 3. For ( 4n ) to be a perfect fourth, ( a+2 ) must be divisible by 4 and ( b ) must be divisible by 4. By solving these conditions simultaneously, the smallest ( n ) that meets all conditions is ( n = 108 ).
Find the smallest positive integer k such that 1176k is a perfect square?
6.
What is the smallest positive integer value of x for which 54x is a perfect square?
324
What is the smallest negative perfect square that is divisible by the four smallest prime numbers?
Perfect squares are positive. A smallest negative number doesn't exist. The four smallest prime numbers are 2, 3, 5 and 7. The smallest perfect square would have to be 2^2 x 3^2 x 5^2 x 7^2 or 44,100
What is the smallest positive integer that 63 can be multiplied by in order for the product to be a perfect square?
63= 9* 7. 9 is already a perfect square, so mulitiply by 7. 7 is your answer.
What is the smallest positive whole number that 150 can be multiplied by to make a perfect square.?
How about 150*6 = 900 which is a perfect square because 30*30 = 900
The number one is the smallest positive square what is the conditional?
If the number is one, then it is the smallest positive square.
