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

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

Are there perfect square factors in 7825? One that should be obvious is 25. Factoring out 25 we get:

Using the property of radicals, we can separate the two factors into their own square roots:

And we can replace the first square root with its value of 5:

(You can check but I don't think 313 has any perfect square factors. If this is true then twe are done.

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).

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):

The digits of 459 also add up to a number divisible by 9:

51 has not perfect square factors so we are finished with the factoring. Now we split up the square root:

I'll leave the last one for you.