Question

How do you simplify `(11y)/sqrt3`?

Answer 1

`(11ysqrt(3))/3`

Explanation:

The simplification required is to remove the root from the denominator of the fraction (so that roots are confined to the numerator).

This may be achieved by multiplying by `1` (so that the value of the overall expression is unchanged), but choosing an appropriately constructed expression that evaluates to `1` (noting that anything divided by itself (excluding zero) equals `1`).

The specially chosen instance of `1` requires a number in its denominator that will remove the root. This can be achieved by multiplying by something divided by `sqrt(3)`, as `sqrt(3) xx sqrt(3) = 3`. To ensure the complete number is `1`, the numerator must also have `sqrt(3)`.

So, the required simplification is

`(11y)/sqrt(3) xx sqrt(3)/sqrt(3)`

`(11ysqrt(3))/3`

Answer 2

`(11y)/sqrt3 = (11y sqrt3)/3`

Explanation:

Simplify by rationalizing the denominator:

`(11y)/sqrt3 xx sqrt3/sqrt3`

`= (11yxx sqrt3)/(sqrt3)^2`

`= (11y sqrt3)/3`