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What is the smallest positive integer value of x for which 54x is a perfect square?
324
What is the smallest integer where the integer before it is a perfect square and the integer after it is a perfect cube?
The integer is 26
Are square roots of positive integers rational?
Only if the integer is a perfect square.
Is the square root of eight rational or irrational?
Irrational. The square root of a positive integer is either an integer (that is, if the integer is a perfect square), or an irrational number.
Is the square root of 39 irrational?
Yes. The square root of a positive integer can only be an integer (if your integer is a perfect square), or an irrational number (if it isn't).
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 integer where the integer before it is a perfect square and the integer after it is a perfect cube?
The integer is 26
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 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 integer greater than 1 that is both a perfect square and perfect cube?
its 81
Are square roots of positive integers rational?
Only if the integer is a perfect square.
Is the square root of eight rational or irrational?
Irrational. The square root of a positive integer is either an integer (that is, if the integer is a perfect square), or an irrational number.
Is the square root of 39 irrational?
Yes. The square root of a positive integer can only be an integer (if your integer is a perfect square), or an irrational number (if it isn't).
What is the smallest positive integer that 248832 can be multiplied by in order for the product to be a perfect square?
The prime factorisation of 248832 is 2¹⁰ × 3⁵ Every perfect square number has a prime factorisation where each prime is to an even power. 2 has an even power 3 has an odd power, so need an extra power → multiple 248832 by 3 which gets (2⁵ × 3³)²
What is the smallest positive perfect square that is divisible by the four smallest numbers?
The four smallest positive integers are 1, 2, 3, and 4. To find the smallest positive perfect square divisible by these numbers, we first determine their least common multiple (LCM). The LCM of 1, 2, 3, and 4 is 12. The smallest perfect square greater than or equal to 12 is 36, which is (6^2). Thus, the smallest positive perfect square that is divisible by 1, 2, 3, and 4 is 36.
What is the least positive integer which should be added to 1350 so that the resulting integer is a perfect square?
The answer is 19.
