Question

How do you simplify `sqrt( 3/10) *sqrt(5/8)`?

Answer 1

`sqrt 3/4`
or `0.433`

Explanation:

`sqrt (3/10).sqrt (5/8)`

Since both fractions are square roots, therefore, taking both fractions under the same root sign

`sqrt (3/10. 5/8)`
or simplifying we obtain `sqrt (3/cancel10_2. cancel5^1/8)`
`=sqrt (3/2. 1/8)`
Multiplying the numerators and denominators respectively
`=sqrt (3/16)`
Now we know that `sqrt 16=4`, we obtain
`=sqrt 3/4`
Inserting the value of `sqrt 3=1.732` in the numerator and dividing with the denominator, we obtain

Answer 2

`1/4 sqrt3`

Explanation:

Using the following :

`• sqrta xx sqrtb = sqrtab hArr sqrtab = sqrta xx sqrtb`

`sqrt( 3/10). sqrt(5/8) = sqrt(3/10 xx 5/8) = sqrt(15/80`

`= sqrt(3/16) = sqrt3/sqrt16 = sqrt3/4 =1/4 sqrt3`