SOLUTION: what is the square root of 7825 and 16524 and 2466

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Question 276871: what is the square root of 7825 and 16524 and 2466
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
Simplifying square roots is a matter of finding factors that are perfect squares.

sqrt%287825%29
Are there perfect square factors in 7825? One that should be obvious is 25. Factoring out 25 we get:
sqrt%2825%2A313%29
Using the property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29 we can separate the two factors into their own square roots:
sqrt%2825%29%2Asqrt%28313%29
And we can replace the first square root with its value of 5:
5sqrt%28313%29
(You can check but I don't think 313 has any perfect square factors. If this is true then twe are done.

sqrt%2816524%29
Again we look for perfect square factors. Since the last two digits are divisible by 4 then the whole number is divisible by 4 (and 4 is a perfect square).
sqrt%284%2A4131%29
Since the digits of 4131 add up to a number which is divisible by 9, then the entire number is divisible by 9 (which is a perfect square):
sqrt%284%2A9%2A459%29
The digits of 459 also add up to a number divisible by 9:
sqrt%284%2A9%2A9%2A51%29
51 has not perfect square factors so we are finished with the factoring. Now we split up the square root:
sqrt%284%29%2Asqrt%289%29%2Asqrt%289%29%2Asqrt%2851%29
2%2A3%2A3%2Asqrt%2851%29
18sqrt%2851%29

I'll leave the last one for you.