√45
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
sqrt(45)=sqrt(9*5)= sqrt(9)*sqrt(5)=3sqrt5
sqrt(ab)=sqrt(a)*sqrt(b)
so I cant use the LCM method? or is it only works using 2 like
√8
2 |__8___
2|__4___
2
2√2
I think used it, rethink what I did. 45=9*5=3*3*5
oh ok thanks
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
√ 27 = √ 9x3 = 3 √ 3
To simplify √45, we need to find the largest square number that can be divided into 45. In this case, it is 9 because 9 is a square number. So, we can rewrite 45 as 9 * 5.
Now, we can take the square root of both factors separately:
√(9) * √(5)
The square root of 9 is 3, so we have:
3 * √(5)
Therefore, the simplified form of √45 is 3√5.
As for your question about why it's not 5√3, let's see how your approach of factoring leads to the same result:
If we rewrite 45 as 5 * 9, we can take the square root of each factor:
√(5) * √(9)
The square root of 5 cannot be simplified any further, so it remains as √(5).
The square root of 9 is 3, so we have:
√(5) * 3
This means that both 3√5 and 5√3 are equivalent expressions for the square root of 45. However, 3√5 is typically considered the simplified form because the number outside the square root sign (in this case, 3) is typically kept as small as possible.