2 of 112 of 11 Items
Question
The product of a multiplication problem is 225−−−√
. What do you know about the factors?(1 point)
Responses
One factor is rational, but the other is irrational.
One factor is rational, but the other is irrational.
They are both rational because the product is rational.
They are both rational because the product is rational.
It cannot be predicted based on the information given.
It cannot be predicted based on the information given.
At least one factor is irrational because the product is irrat
ional.
ional.
The other factor could be either rational or irrational.
To determine what you know about the factors when the product of a multiplication problem is the square root of 225 (√225), you can find the factors of 225 and analyze their properties.
To find the factors of 225, you can start by finding its prime factorization. The prime factorization of 225 can be written as 3^2 * 5^2.
Now, we can list the factors of 225 by combining different combinations of its prime factors:
1, 3, 5, 9, 15, 25, 45, 75, 225
Looking at these factors, we can conclude that at least one factor is irrational. This is because there are factors like √225 (which equals 15) that are rational, but there are also factors like √9 (which equals 3) that are irrational.
Therefore, the correct response is:
"At least one factor is irrational because the product is irrational."