Question 118001: express 5√72 in simplest radical form
√ = radical sign
find the sum of: √120 + √75
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! #1
 Start with the given expression
Let's simplify 
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
Now reintroduce the 5 to get  . Now multiply to get
So simplifies to
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Check:
Notice if we evaluate with a calculator we get
and if we evaluate we get
This shows that  . So this verifies our answer
#2
 Start with the given expression
 Factor 120 into 15*8 and factor 75 into 15*5
 Break up the square roots
 Factor out the common term of 
So simplifies to
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