Question

Simplify. Assume that all expressions under radicals represent nonnegative numbers
√36x^4y^10

Answer 1

can you factor 36 into its primes?

Answer 2

you mean 6.6 ?

Answer 3

thats a start, but 6 isn't prime

Answer 4

what's a prime?

Answer 5

a number that cannot be divided evenly by another number (just 1 and itself)
2,3,5,7,11,13...

Answer 6

6.6 would work (in this case) but I want to show you how I do these
a way that works for all of them

Answer 7

Like 4√9

Answer 8

I look at that stuff as:
36x^4y^10 = 2.2.3.3.x.x.x.x.y.y.y.y.y.y.y.y.y.y
two 2s two 3s four Xs and ten Ys

Answer 9

then, to get the square root down to size, pull out as many pairs as you can

Answer 10

is this helping or confusing?

Answer 11

Both

Answer 12

well there is one pair of 2s so we have
2√3.3.x.x.x.x.y.y.y.y.y.y.y.y.y.y

Answer 13

then a pair of 3s
2.3√x.x.x.x.y.y.y.y.y.y.y.y.y.y

Answer 14

then two pairs of Xs
2.3.x.x√y.y.y.y.y.y.y.y.y.y
and five pairs of Ys
2.3.x.x.y.y.y.y.y√1

Answer 15

so now I count and see
6 x^2 y^5 (and nothing left under the radical)

Answer 16

I multiply all the numbers I could pull out, and count the letters to get the exponents
just another way to look at it... hope I didn't confuse you too much

Answer 17

Is √36x^4y^10=6 x^2 y^5

Answer 18

it should be, what do you get when you square it?

Answer 19

@jupiter , you are correct.