root20 + root45 (simplify)?

I'm going to use the symbol | to represent square roots (sorry can't easily get square root sign on my keyboard)

* = times or multiplied by

|20 + |45

= |4*|5 + |9*|5
= 2*|5 + 3*|5
= 5*|5
= 5|5

Answer = 5|5, or "5 root 5"

2sqrt(5) + 3sqrt(5) = 5sqrt(5)
=
5^(3/2)

root20=root4*5=2sqrt5
root45=root9*5=3sqrt5
you can add sqrts together if they are the same thing inside like right now they have root5 (treat them like variables) and add the coefficients so that would be 5sqrt5

proof on a calculator
root20+root45=11.18033989...
5sqrt5=11.18033989...

2root5 + 3root5
equals 5root5

Message for more info...

√20 + √45
2√5 + 3√5
5√5

We need to get the numbers under each of the roots to be the same before we can do our addition - kind of like adding fractions, only we're making them more simplified and THEN getting a common factor (assuming we can't in the first step).

Q: √20 + √45

Consider √20:
√20 = √4 * √5
So: = 2√5

Consider √45:
√45 = √9 * √5
So: = 3√5

Now the question can be rewritten as:
2√5 + 3√5

Luckily, we have common factors so it's as easy as adding them together now.

2√5 + 3√5 = 5√5

5√5 cannot be simplified any further, so we leave the answer as this.

Hope this helped you.

√20 + √45
= √(2^2 x 5) + √(3^2 x 5)
= 2√5 + 3√5
= (2 + 3)√5
= 5√5

√20 + √45 = √(4)(5) + √(9)(5) = 2√5 + 3√5 = 5√5

sqrt(20) + sqrt(45) = sqrt(4 * 5) + sqrt(9 * 5) =
= sqrt(4)*sqrt(5) + sqrt(9)*sqrt(5) = 2sqrt(5) + 3sqrt(5) = 5sqrt(5)