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Given:
Joey had 26 game cards.
His friend Richard gave him some more, and now Joey has 100 cards.
To find:
How many cards did Richard give to Joey?
Solution:
Let x be the number of cards that Richard give to Joey.
Joey had 26 game cards.
Now, the total cards joey has
Joey has total 100 cards.
Therefore, Richard gave him 74 cards.
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.