SOLUTION: 1. Please help Simplify 2/(sqrt(20)) 2. The simplfied version of sqrt(24/36) is sqrt(6)/6. true or false

Question 228111: 1. Please help Simplify 2/(sqrt(20))
2. The simplfied version of sqrt(24/36) is sqrt(6)/6. true or false
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
1. Simplify
Part of simplifying square roots is making sure the denominator is rational. IOW, do not leave square roots in denominators. Your denominator is a square root so we need to get rid of it. We do so by multiplying the numerator and denominator by any expression that will turn the square root(s) in the denominator into square root(s) of perfect square(s). With a monomial (one term) denominator like yours this is not difficult. You can always turn a monomial denominator into a perfect square by multiplying it by itself. In this case we can multiply the numerator and denominator by . But if we're clever, we'll realize that multiplying by will work, too. And since this way saves us some work, this is the path we'll follow:

(Note: If we had used and fully and correctly simplified the result we would end up with the same answer.)

2. The simplified version of sqrt(24/36) is sqrt(6)/6. true or false
Let's simplify and see. There are several paths we can take. Since I see a perfect square denominator, 36, I am going to use the following property of square roots, , to split the square root of the fraction into a fraction of square roots:

Since :

Another part of simplifying square roots is to make sure that no perfect square factors remain inside the square roots. Since 4 is a perfect square and 4 is a factor of 24, we will use the following property of square roots, , to simplify the numerator:

And we are done simplifying. So is equal to ? Answer: No.
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