√45

Question

i dont understand the answer = 3√5
Using Least common multiple
3 |__45___
3 |__15___
5

why not 5 √3

i know that √45 could be √9x5 = 3√5

Answer 1

sqrt(45)=sqrt(9*5)= sqrt(9)*sqrt(5)=3sqrt5

sqrt(ab)=sqrt(a)*sqrt(b)

Answer 2

so I cant use the LCM method? or is it only works using 2 like
√8

2 |__8___
2|__4___
2

2√2

Answer 3

I think used it, rethink what I did. 45=9*5=3*3*5

Answer 4

oh ok thanks

Answer 5

You are really just looking for a perfect square hiding under the square root sign. The square root of 45 has 5 x (the perfect square 9). The square root of 9 moves to the front of the root sign, as it is perfect (the square root of 9 is 3).
A second example.
The square root of 27
Under the root sign is the perfect square 9 then times by 3, so the square root of 9 comes to the front of the square root, leaving 3 root 3

Answer 6

√ 27 = √ 9x3 = 3 √ 3