what is the smallest number that 54 can be multiplied by to give a perfect square?
all perfect squares have pairs of equal factors
e.g. 400
= 2x2 x 10x10
54 = 2 x 3 x 3 x 3
so we need another 2 and another 3
so the smallest number to be multiplied by 54 so it becomes a perfect square is 6
check:
6x54 = 324 = 18^2
Hmm, let's put a smile on our faces and figure this out! To find the smallest number that 54 can be multiplied by to give a perfect square, we need to look at its prime factorization. 54 can be written as 2 * 3^3.
To make it a perfect square, we have to balance the exponents of the prime factors. The smallest number that comes to my mind is 3, so if we multiply 54 by 3, we get 162, which is equal to 2 * 3^4.
Voilà! 162 is a perfect square because the exponents are balanced. Keep in mind, I'm just clowning around with numbers, so I hope this brings a bit of laughter to your day!
To find the smallest number that 54 can be multiplied by to give a perfect square, we need to factorize 54.
The prime factorization of 54 is:
54 = 2 x 3 x 3 x 3
To make it a perfect square, we need to have an even power of each prime factor.
Since 2 appears once in the factorization, we need to multiply 54 by an additional 2 to make its power even.
Therefore, the smallest number that 54 can be multiplied by to give a perfect square is:
54 x 2 = 108
To find the smallest number that 54 can be multiplied by to give a perfect square, we need to find the square root of 54.
To do this, you can use a calculator or mathematical software. Alternatively, you can find an approximate value by finding the square root of a nearby perfect square.
The square root of 54 is approximately 7.348. Since we are looking for a perfect square, we need to find the smallest whole number that can be multiplied by 7.348 to obtain a perfect square.
The smallest whole number that can be multiplied by 7.348 to give a perfect square is 4. By multiplying 54 by 4, we get 216, which is a perfect square since the square root of 216 is 14.
So, the answer is 4.