simplifying

Question

When I was looking at an example I understood it all and it helped greatly but what confused me was the very end answer when the fraction was simplified.   How does +-(9/25) simplify to +-(3/5)

The y is squared

Answer 1

I assume the problem is (if not, please clarify):

 

y² = 9/25

 

Well 9 = 3² and 25 = 5², so we can write the equation as:

 

y² = 3²/5² = (3/5)²

 

To find y, take the square root of both sides:

 

√y² = √(3/5)²

 

y = ±3/5

Answer 2

when you take the square root of a fraction you get a new fraction where the numerator is the square root of the original numerator and the denominator is the square root of the original denominator. In other words, you take the square root of the numerator and denominator separately 

 

Mathematically we write in general terms    √(a/b) = √a/√b        (of course b is not zero)

 

In your example Sq. root 9/25 = sq. root 9 / sq root 25 = 3/5

 

Depending on the circumstances the answer is +/- but if we want the principal root it refers to the positive root.