Question

How do you rationalize the denominator and simplify `1/sqrty`?

Answer 1

`1/sqrt(y)-=sqrt(y)/y`

The `-=` means 'equivalent to'.

Explanation:

Mathematicians do not like a root to be in the denominator if at all possible. Consequently you should always look to remove it if able. Unless instructed otherwise.

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Multiply by 1 and you do not change the value. However the value of 1 comes in many forms so you may change the way something looks without changing its intrinsic value.

Given:`" "1/sqrt(y)`

Multiply by 1 but in the form of `1=sqrt(y)/sqrt(y)` giving:

`" "1/sqrt(y)xxsqrt(y)/sqrt(y) = sqrt(y)/y`

Hence the rationalised denominator condition is:`" "sqrt(y)/y`