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Q: Find the smallest positive integer k such that 1176k is a perfect square?

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The integer is 26

63= 9* 7. 9 is already a perfect square, so mulitiply by 7. 7 is your answer.

Only if the integer is a perfect square.

its 81

the answer is 144, it is divisible by 1, 4, 9, 16, 36, and 144.

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).

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.

The answer is 19.

17

Yes it is.Since the square of an integer is called a perfect square, then the square root of a perfect square must be an integer.

There are two square roots of a perfect square: a positive number and the same number as a negative number. The square root of a perfect square will always be an integer.

A perfect square is a square of an integer (a whole number).

In terms of prime factors, 1008 = 24*32*7 Then since 24 and 32 are perfect squares, all that is required is to make 7q a perfect square and so q = 7.

Find the square root of the number.Take the integer part of the answer.Square the integer part.Subtract this square from the original number.

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

A perfect square has the condition that it must be any positive integer multiplied by itself. The closest perfect squares to 50 are 7*7 = 72 = 49 and 8*8 = 82 = 64 since 50 lies between 49 and 64, it must be it is not the square of a positive integer and, therefore, is not a perfect square.

The smallest integer is 2.There is no smallest number. Dividing 1152 by any number of the form x = 1/(2k2) where k is an integer will result in a perfect square. Since there is no limit to how large k can be, there is no limit to how small x can be.

(3x5x7x11)2 =1334025

It is the square of an integer: that is what a perfect square is.

A perfect square is the square of an integer, i.e., an integer multiplied by itself. For example, 25 is a perfect square, because 5 x 5 = 25. But, in literal mathematical terms, a perfect number is a positive integer that is the sum of its proper positive divisors, excluding the number itself. A square number is also called a "perfect square", so an example of a square number is above. So, a perfect square number would have to be a number that is both perfect and square, and there are yet to be any of these numbers "discovered".

an integer

No. However, the square root of any positive integer that is NOT a perfect square, IS irrational.

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!

The square root of 2 is irrational. In general, the square root of a positive integer is either an integer (if you take the square root of a perfect square), or it is irrational.

It is a natural number. It is a positive integer. It is a positive rational number. It is a positive real number. It is a perfect square. It is a three digit integer. It is a palindromic integer. Probably many other sorts.