Question

What is the simplification of `sqrt((18x^5y^4)/(49xz^3))`?

Answer 1

`(3x^2y^2sqrt(2z))/(7z^2)`

Explanation:

`color(blue)("General comment")`

Any values that are squares can be taken outside the square root. So for example if you had `sqrt(2^2xx3)` you could write this as
`2sqrt(3)`. Or if you had `sqrt(2^4xx3)` you could write `2^2sqrt(3)`

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`color(blue)("Answering the question")`

Write as `sqrt(2xx3^2xx x xx x^4xx y^4)/(sqrt(7^2 xz xx z^2)` giving:

`(3x^2y^2sqrt(2x))/(7zsqrt(xz))`

Write as:`" "(3x^2y^2sqrt2cancel(sqrtx))/(7zsqrtz cancel(sqrtx))`

Multiply by 1 but in the form of `1=sqrtz/sqrtz` giving

`(3x^2y^2)/(7z)xxsqrt(2)/sqrt(z) xx sqrtz/sqrtz`

`(3x^2y^2sqrt(2z))/(7z^2)`