SOLUTION: express in radical form, what is the product of 2 x the square root of 7 and 3 x the square root of 5

Algebra ->  Square-cubic-other-roots -> SOLUTION: express in radical form, what is the product of 2 x the square root of 7 and 3 x the square root of 5      Log On


   

Question 280783: express in radical form, what is the product of 2 x the square root of 7 and 3 x the square root of 5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Asqrt%287%29%29%2A%283%2Asqrt%285%29%29
Since this is all multiplication and since multiplication is Commutative and Associative we can change the order and grouping any way we choose:
%282%2A3%29%28sqrt%287%29%2Asqrt%285%29%29
For the square roots we can use the property of radicals, root%28a%2C+p%29+%2A+root%28a%2C+q%29+=+root%28a%2C+p%2Aq%29 to multiply them:
6sqrt%2835%29
The only thing left is to simplify the square root, if possible, by factoring out perfect squares. But 35 has no perfect square factors so it will not simplify.