Page 12 - NUMINO Challenge_D2
P. 12
Basic Concepts Square Number and Exponent
A number multiplied by itself, such as 1( 1 1), 4( 2 2), 9( 3 3), and
16( 4 4), is called a square number.
Since a square number is the product of two identical numbers, each prime
number found from the prime factorization of a square number is multiplied
an even number of times.
100 10 10 2 2 5 5 144 12 12 2 2 2 2 3 3
two two four two
When multiplying an identical number many times, the number can be raised
to an exponent by writing how many times the number is multiplied in the
upper right corner.
2 2 22 3 3 3 3 34 2 5 5 2 52 2 2 2 3 3 23 32
Example What is the smallest number that should be multiplied in order to
make 28 a square number?
Class Notes
The prime factorization of 28 is 28 .
In order to be a square number, each prime number found from the prime
factorization should be multiplied an (even, odd) number of times.
2 is multiplied twice, and 7 is multiplied time(s), which is an (even, odd)
number of times. Therefore, if is multiplied one more time, 7 is multiplied an
even number of times. This would make 28 7 196 14 14.
Therefore, is the smallest number that should be multiplied in order to make 28 a
square number.
Try It Again What is the smallest number that should be multiplied in order
to make 135 a square number?
9Number and Operations
A number multiplied by itself, such as 1( 1 1), 4( 2 2), 9( 3 3), and
16( 4 4), is called a square number.
Since a square number is the product of two identical numbers, each prime
number found from the prime factorization of a square number is multiplied
an even number of times.
100 10 10 2 2 5 5 144 12 12 2 2 2 2 3 3
two two four two
When multiplying an identical number many times, the number can be raised
to an exponent by writing how many times the number is multiplied in the
upper right corner.
2 2 22 3 3 3 3 34 2 5 5 2 52 2 2 2 3 3 23 32
Example What is the smallest number that should be multiplied in order to
make 28 a square number?
Class Notes
The prime factorization of 28 is 28 .
In order to be a square number, each prime number found from the prime
factorization should be multiplied an (even, odd) number of times.
2 is multiplied twice, and 7 is multiplied time(s), which is an (even, odd)
number of times. Therefore, if is multiplied one more time, 7 is multiplied an
even number of times. This would make 28 7 196 14 14.
Therefore, is the smallest number that should be multiplied in order to make 28 a
square number.
Try It Again What is the smallest number that should be multiplied in order
to make 135 a square number?
9Number and Operations
