square root 18x^2y^3?

Question

simplify asumming all are postive numbers

Answer 1

We have this guy:

square root 18x^2y^3 and we must simplify.

Let's place each term inside their own radicand.

We get this:

sqrt{18} = sqrt{9} times sqrt{2} = 3(sqrt{2})

sqrt{x^2} = x

sqrt{y^3} = sqrt{y^2} times sqrt{y} = y(sqrt{y})

Put everything together:

3xy(sqrt{2y})

Guido

Answer 2

sqrt ( 18x^2 y^3)

Use the square root property

sqrt(abc) = sqrt(a)sqrt(b)sqrt(c)

sqrt(18) sqrt(x^2) sqrt(y^3)

Note that 18 = 9 x 2, and y^3 = (y^2)y

sqrt(9*2) sqrt(x^2) sqrt( (y^2) (y) )

We can split up square roots as sqrt(ab) = sqrt(a)sqrt(b).

sqrt(9) sqrt(2) sqrt(x^2) sqrt(y^2) sqrt(y)

We know the square root of 9, and we know the square root of a squared term like y^2. Therefore, our simplification becomes

3sqrt(2) (x) (y) sqrt(y)

3xy sqrt(2)sqrt(y)

Combine sqrt(2) and sqrt(y) by multiplying their insides.

3xy sqrt(2y)

Answer 3

sqrt(18x^2y^3)
= sqrt(9)*sqrt(2)*sqrt(x^2)*sqrt(y^3)
= 3*sqrt(2)*x*sqrt(y^2)*sqrt(y)
= 3xy*sqrt(2)*sqrt(y)
= 3xy*sqrt(2y)

Remember, the sqrt(ab) = sqrt(a)*sqrt(b), so you can break these things apart into entities you know how to directly take the square root of.

--charlie

Answer 4

Ans> 3x sqrt2y