Question

What is the simplest form of the expression? sqrt 20+ sqrt 45 - sqrt 5

Answer 1

4√5 Is the simplest form

Answer 2

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. =)