Question

How do you simplify `sqrt45+sqrt80`?

Answer 1

`sqrt(40)+sqrt(80)=color(red)(7sqrt(5))`

Explanation:

`45=5xx9=5xx3^2color(white)("xxx")rarrcolor(white)("xxx")sqrt(45)=3sqrt(5)`

`80=5xx16=5xx4^2color(white)("xx")rarrcolor(white)("xxx")sqrt(80)=4sqrt(5)`

`rArr sqrt(40)+sqrt(80`

`color(white)("XXX")=3sqrt(5)+4sqrt(5)`

`color(white)("XXX")=7sqrt(5)`

Answer 2

`7sqrt5`

Explanation:

`sqrt45+sqrt80`

`:.=sqrt(3*3*5)+sqrt(2*2*2*2*5)`

`:.sqrt2xxsqrt2=2`

`:.sqrt3xxsqrt3=3`

`:.=3sqrt5+4sqrt5`

`:.=7sqrt5`

~~~~~~~~~~~
check:-

`sqrt45=6.708203933+sqrt80=8.94427191`

`6.708203933+8.94427191=15.65247584`

`7sqrt5=15.65247584`