Question

What is `8sqrt48 - 6sqrt75 + 7sqrt80`?

Answer 1

`8sqrt48-6sqrt75+7sqrt80=2sqrt3+28sqrt5`

Explanation:

To simplify `8sqrt48-6sqrt75+7sqrt80`, let us first factorize numbers within square root sign i.e. `48`, `75` and `80`.

As `48=2xx2xx2xx2xx3`, `75=3xx5xx5` and `80=2xx2xx2xx2xx5`,

`8sqrt48-6sqrt75+7sqrt80 =`

`8sqrt(ul(2xx2xx2xx2)xx3)-6sqrt(3xxul(5xx5))+7sqrt(ul(2xx2xx2xx2)xx5)`

= `8xx2xx2xxsqrt3-6xx5xxsqrt3+7xx2xx2xxsqrt5`

= `32sqrt3-30sqrt3+28sqrt5`

= `2sqrt3+28sqrt5`