Question 118551: Simplify the expression.
1a) square root of 54
1b)square root of 72
1c) square root of 5/9
1d) square root of 7/36
1e) square root of 9/11
1f)square root of 9/25
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first three to show you how to do these problems
1a)
 Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.
So let's list the factors of 54
Factors:
1, 2, 3, 6, 9, 18, 27, 54
Notice how 9 is the largest perfect square, so lets factor 54 into 9*6
 Factor 54 into 9*6
 Break up the square roots using the identity 
 Take the square root of the perfect square 9 to get 3
So the expression simplifies to
----------------------------
Check:
Notice if we evaluate the square root of 54 with a calculator we get
and if we evaluate we get
This shows that  . So this verifies our answer
1b)
 Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.
So let's list the factors of 72
Factors:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Notice how 36 is the largest perfect square, so lets factor 72 into 36*2
 Factor 72 into 36*2
 Break up the square roots using the identity
 Take the square root of the perfect square 36 to get 6
So the expression simplifies to
----------------------------
Check:
Notice if we evaluate the square root of 72 with a calculator we get
and if we evaluate we get
This shows that  . So this verifies our answer
1c)
 Start with the given expression
 Break up the fraction
 Take the square root of 9 to get 3
So simplifies to
|
|
|
