SOLUTION: please help me solve these fololowing questions: simplify the following radicals: squar foot of 245 squar foot of 80 and the missing length of the triangle (right trian

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Question 12600: please help me solve these fololowing questions:
simplify the following radicals:
squar foot of 245
squar foot of 80
and the missing length of the triangle (right triangleS)
A= 8 B=12 what is C?
A-2 C=squar foot of 13 B=?

Answer by AdolphousC(70) About Me  (Show Source):
You can put this solution on YOUR website!
In order to simplfy square roots of non perfect squares ( 16, 25, 36 are perfect squares ) the easiest thing to do is to break your number down into its prime factors.


Prime numbers are those numbers which only are divisable by 1 and itself. 5 is prime, because only 1 and 5 divide into 5 evenly. However, 9 is NOT prime because 3 also divides into 9.


So to prime factor 245, we need to find its prime factors, the prime factors of 245 are 7, 7, 5 we know this because 7*7*5 = 245.


A rule of radicals states that sqrt%287%2A7%2A5%29 = sqrt%287%2A7%29 * sqrt%285%29
Now simplfy each square root, sqrt%287%2A7%29+=+7+and sqrt%285%29 can not be simplfied
Mulply the two together and you get 7%2Asqrt%285%29


sqrt%2880%29 is the same, the prime factors of 80 are (2*2*2*2*5)
Rewrite as sqrt%282%2A2%29+%2A+sqrt%282%2A2%29+%2A+sqrt%285%29
Simply 2+%2A+2+%2A+sqrt%285%29+=+4%2Asqrt%285%29


Now, as for the missing length of right triangles, you must use the pythagorean therom a%5E2+%2B+B%5E2+=+C%5E2
Plug in what you know 8%5E2+%2B+12%5E2+=+C%5E2
Simplfy 64+%2B+144+=+C%5E2
Simplfy 208+=+c%5E2
so C+=+sqrt%28208%29 and use the process from above to simplfy sqrt%28208%29


For the last problem, I am assuming that A = 2 since a length of a triangle leg can not be negative,
2%5E2+%2B+B%5E2+=+%28sqrt%2813%29%29%5E2
The square of any square root is the number so we have
4+%2B+B%5E2+=+13
B%5E2+=+9
B+=+3