Question

How do you simplify `sqrt(1) / sqrt (7) times sqrt(7) / sqrt(11)`?

Answer 1

`=sqrt11 / 11`

Explanation:

`(sqrt1 / color(blue)(sqrt7)) * (color(blue)(sqrt7) / sqrt11)`

We can observe that `color(blue)(sqrt7` is present in denominator of first term and numerator of second and hence can be cancelled.

`=(sqrt1 / cancelsqrt7) * (cancelsqrt7 / sqrt11)`

`=sqrt1/sqrt11`

Now we rationalise the expression by multiplying the numerator and denominator of the expression by `sqrt11`

`=(sqrt1 * color(blue)(sqrt11))/(sqrt11 * color(blue)(sqrt11)`

`=(sqrt11)/(sqrt (11 *11)`

`=(sqrt11)/(sqrt (11 ^2)`

`=sqrt11 / 11`