$\sqrt{45}+\sqrt{125} = 3\sqrt 5 + 5 \sqrt 5 = 8\sqrt 5 = \sqrt{8^2\times 5} = \sqrt{320}$ . Therefore, $n = \boxed{320}$ .

There are two simple ways to solve this problem.

1

Recall that √a√b=√ab

√45+√125=√n

√9x5+√25x5=√n

√9√5+√25√5=√n

3√5+5√5=√n

8√5=√n

√64√5=√n

√64x5=√n

√320=√n

320=n

2

Recall that (a+b)^2=a^2+2ab+b^2

√45+√125=√n

(√45+√125)^2=n

(√45)^2+2(√45)(√125)+(√125)^2=n

45+2(√5625)+125=n

170+2(75)=n

170+150=n

320=n

I prefer the first way because you don't need to know the square root of such a big number (5625)

sqrt(45)+sqrt(125)=sqrt(9 x 5)+sqrt(25 x 5)

= sqrt(9) x sqrt(5) + 5 x sqrt(5)

=3 x sqrt(5)+5 x sqrt(5)

sqrt(5) (3+5)

8 sqrt(5)

square this, and you get

64 x 5

=320