Math help please!!?

Question

could someone help me with these problems?? ^ this means to the power of ..

Thanks



1. square root 200x ^2 y
100xy
20x square root y
100x square root 2y
10x square root 2y

2. simplify square root 72x^4 y^5

6x^2y^2 square root 2y
2x^2y^ square root 18y
34x^2y^2 square root y
6x^2y square root 2y^3

3. Multiply and simplify (4 square root 10x64y62) (2square root 10x62y^2)

8 square root 100x^6y^4
80 square root x^6y^4
80 x^3y^2
or already simplified.

Answer 1

Remember that √(ab) = (√a)(√b). You want to factor what's inside to get as many perfect squares together as you can, so that you can move these outside of the radical.

So with √(200 x² y), notice that the x² can come right out, leaving you with x√(200y). The 200 can be broken down into 2*100, so x√(200y) = x√(2*100y) = x√(2*10² y) = 10x√(2y). This is as simple as you can get it, and it matches one of our choices.

For the second one:
√(72x^4 y^5) =
x² √(72 y^5) =
x² √(72 y*y^4) =
x²y² √(72 y) =
x²y² √(36*2 y) =
6x²y² √(2y)

For the third one, use the √(ab) = (√a)(√b) rule in reverse to combine the square roots, giving you 4*2 times a big square root. Then combine terms inside and simplify.

Answer 2

For the first one, square each of them and see which one comes out right. Well, the ones with 100 in them are obviously wrong, since the square of 100 is 10,000, which is a lot bigger than 200.

For #2, some of them are just wrong. Beyond that, if there's a power of x or y inside the square root sign that's bigger than 1, it's not simplified.

For the same reason, in #3 only one of the answers is possibly right.

Answer 3

1. 10x square root 2y
2. 6x^2y^2 square root 2y
3. Didn't got ur third question clearly