In the prime factorisation of a perfect square in power format, all primes must be to an even power.
5688 = 23 x 32 x 79
To convert this it a perfect square, it needs the 2 and 79 to have an even power - the 3 is already at an even power.
The smallest way to do this is to multiply 5688 by 2 x 79, ie multiply it by 158.
5688 x 158 = 23 x 32 x 79 x 2 x 79
= 24 x 32 x 792
= (22 x 3 x 79)2
= (948)2
= 898704
the answer is 144, it is divisible by 1, 4, 9, 16, 36, and 144.
(3x5x7x11)2 =1334025
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
perfect square
A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.Integers are rational numbers so the square [which is an integer] is a rational number.
6.
324
5
The integer is 26
You multiply an integer by itself twice or multiply 1 by an integer three times.
the answer is 144, it is divisible by 1, 4, 9, 16, 36, and 144.
63= 9* 7. 9 is already a perfect square, so mulitiply by 7. 7 is your answer.
its 81
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
Any time you multiply an integer with itself, the product is a perfect square.
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.
The answer is 19.