Question

What is the fully simplified answer to sqrt(7/18) + sqrt(5/8) - sqrt(7/2)

Answer 1

`=(-4√(7)+3√(5))/(6√(2))`

Explanation:

Given expression as:

`=\sqrt{(7)/(18)}+\sqrt{(5)/(8)}-\sqrt{(7)/(2) }`

We need to simplify the given expression.

Solution:

We have:

`=\sqrt{(7)/(18)}+\sqrt{(5)/(8)}-\sqrt{(7)/(2) }`

Rewrite the expression as:

`=(√(7))/(3√(2)) - (√(7))/(√(2)) +(√(5))/(2√(2))`

`(√(7))/(√(2) )` is a common factor to the first two terms.

Using distributive property we can factor out
`(√(7))/(√(2) )` from the first two terms.

`=(√(7))/(√(2))((1)/(3) -1) +(√(5))/(2√(2))`

`=(√(7))/(√(2))((1-3)/(3)) +(√(5))/(2√(2))`

`=(√(7))/(√(2))((-2)/(3)) +(√(5))/(2√(2))`

`=-(2√(7))/(3√(2)) +(√(5))/(2√(2))`

`√(2)` is common factor, so we can factor
`√(2)` from the above expression.

`=(1)/(√(2) )( -(2√(7))/(3) +(√(5))/(2))`

`=(1)/(√(2) )( (-2* 2√(7)+3* √(5))/(6))`

`=(1)/(√(2) )( (-4√(7)+3√(5))/(6))`

`=(-4√(7)+3√(5))/(6√(2))`

Therefore, we get simplified answer as.

`=(-4√(7)+3√(5))/(6√(2))`