Question

Rationalize the denominator and simplify if possible. Assume that all variables represent positive numbers. x6y⎯⎯⎯⎯√

Answer 1

The rationalized form of
`\((√(x))/(6y)\) is`
`(√(xy) )/(6y^2)`

To rationalize the denominator and simplify the expression √x/6y, we need to eliminate the square root from the denominator. To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is 6y.

This gives us (√x/6y) * (6y/6y)

= √x * 6y / (6y * 6y)

= 6√xy / 36y²

= √xy / 6y²

So, the rationalized and simplified expression is
`(√(xy) )/(6y^2)`

Therefore, the rationalized form of the expression
`\((√(x))/(6y)\) is`
`(√(xy) )/(6y^2)`.

Complete question:

Rationalize the denominator and simplify if possible. Assume that all variables represent positive numbers. √x/6y