Question 238194: Write each of the following square roots in the form a√b, where a and b are integers and b has the least value possible. For example, √180=6√5.
1. √360
2. √40
3. √240
Please, please help! Thank you.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The process needed is to complete the prime factorization of the radicand.
360, even so divisible by 2
180, even so divisible by 2
90, even so divisible by 2
45, not even, but digits sum to 9 which is divisible by 3, so is divisible by 3
15, digits sum to 6, so divisible by 3
5, prime.
Prime factors are 2, 2, 2, 3, 3, 5. Take out one pair of 2s and one pair of 3s leaving a 2 and a 5. 2 times 3 is 6 and 2 times 5 is 10 so:
John
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