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1 answer:
Answer:
Step-by-step explanation:
First, you must observe the figure attached.
You can identify that:
Then, you can solve for the variable "x" in order to find its value. Then, you get that this is:
You can also identify in the figure that:
Since you know the value of "x", you can substitute it into the equation:
Finally, you must solve for the variable "y" in order to find its value. So, you get:
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If 60 is a factor of n², then √60 is a factor of n. However, n is a whole number, so its factors are whole numbers.
Simplify √60:
If 2√15 is a factor of a whole number n, then √15 must be another factor to make it a whole number.
If 60 is a factor of n², then 2, 3, and 5 must be factors of n. The factors of n² are the squares of the factors of n, so 2, 2, 3, 3, 5, and 5 must be factors of n².
Now, if 2, 2, 3, 3, 5, and 5 are factors of n², then:
* 5×5=25 must also be its factor
* 2×2×3×3=36 must also be its factor
* 2×2×5×5=100 must also be its factor
Only 16 may not be a factor of n². The answer is A.
Simplify √60:
If 2√15 is a factor of a whole number n, then √15 must be another factor to make it a whole number.
If 60 is a factor of n², then 2, 3, and 5 must be factors of n. The factors of n² are the squares of the factors of n, so 2, 2, 3, 3, 5, and 5 must be factors of n².
Now, if 2, 2, 3, 3, 5, and 5 are factors of n², then:
* 5×5=25 must also be its factor
* 2×2×3×3=36 must also be its factor
* 2×2×5×5=100 must also be its factor
Only 16 may not be a factor of n². The answer is A.