Question

How do you simplify (square root of 6/square root of 7) * (square root of 14/square root of 3)?

Answer 1

Write the roots as their factors..

Explanation:

`(sqrt6/sqrt7)*(sqrt14/sqrt3)`
Because we are multiplying the two fractions, we know that we can simplify by cancelling right?
Write each of the fractions, if possible, in their factors . For example : `sqrt6=sqrt2*sqrt3`

You should get this : `((sqrt2*sqrt3)/sqrt7)*((sqrt7*sqrt2)/sqrt3)`
Cancel out any factor that is both in the numerator and the denominator.
You should be left with root 2 times root 2, which is 2 :)

Answer 2

`2`

Explanation:

`sqrt6/sqrt7*sqrt14/sqrt3`

`:.=sqrt84/sqrt21`

`:.=sqrt(2*2*3*7)/sqrt21`

`:.sqrt2*sqrt2=2`

`:.=(2sqrt(3*7))/sqrt21`

`:.=(2cancelsqrt21^1)/cancelsqrt21^1`

`:.=2`