First, find the prime factorization of 20, 45 and 5:
20 | 2
10 | 2 ⇒ 20 = 2² · 5
5 | 5
1 |
45 | 3
9 | 3 ⇒ 45 = 3² · 5
5 | 5
1 |
And last, the prime factorization of 5 is 5 itself (5 is a prime number).
So,
√20 + √45 – √5 = √(2² · 5) + √(3² · 5) – √5
√20 + √45 – √5 = √(2²) · √5 + √(3²) · √5 – √5
√20 + √45 – √5 = 2 · √5 + 3 · √5 – √5
√20 + √45 – √5 = (2 + 3 – 1) · √5
√20 + √45 – √5 = 4 · √5 <——— this is the simplest form.
I hope this helps. =)
