Question

Which expression is equivalent to sqrt128x^5y^6/2x^7y^5 ? Assume x 0 and y > 0.

Answer 1

`(8√(y))/(x)`

Explanation:

`\sqrt{(128x^5y^6)/(2x^7y^5)}`

we have division inside the square root .

LEts simplify it

128 divide by 2 is 64

use property of exponents to simplify the exponents

`(a^m)/(a^n) =a^(m-n)`

`(x^5)/(x^7) =x^(5-7)=x^(-2)`

`(y^6)/(y^5) =y^(6-5)=y`

`\sqrt{(128x^5y^6)/(2x^7y^5)}`

`\sqrt{(64x^(-2)y)/(1)}`

To make the exponent positive move x to the denominator

`\sqrt{(64y)/(x^2)}`

Now we take square root

square root (64) is 8

square root of x^2 is x

`(8√(y))/(x)`

Answer 2

`(8√(y) )/(x)`

Explanation:

We are given the following expression and we are to simplify it:

`\sqrt {\frac {128x^5y^6} {2x^7y^5} }`

To make it easier to solve, we can also write this expression as:

`\sqrt {(128)/(2) * \frac {x^5} {x^7} * \frac {y^6} {y^5}}`

Now we will cancel out the like terms to get:

`\sqrt {64*\frac{1} {x^2}*y }`

Taking the square root of the terms to get:

`8*\frac {1}{x} .√(y)`

`(8√(y) )/(x)`