QuestionSimplify.
Studdy Solution
STEP 1
What is this asking? We're asked to simplify an expression with a bunch of square roots! Watch out! Don't forget to simplify the radicals completely before combining them.
STEP 2
1. Simplify the first term.
2. Simplify the second term.
3. Combine like terms.
STEP 3
Alright, let's **break down** that first term, .
We want to find the **largest perfect square** that divides 45.
That's **9**, since .
STEP 4
So, we can rewrite as .
Using the **product property of square roots**, this becomes .
STEP 5
Since is just **3**, our simplified first term is .
Awesome!
STEP 6
Now, let's **tackle** the second term, .
We're looking for the **largest perfect square** that divides 20.
That's **4**, because .
STEP 7
We can rewrite as .
Using that handy **product property** again, we get .
STEP 8
Since is **2**, our simplified second term becomes , which is .
Fantastic!
STEP 9
Now, let's **bring it all together**!
Our original expression is .
STEP 10
After simplifying the first two terms, we have .
Notice how they all have that in common?
That means they're **like terms**, like having three apples, adding six apples, and then taking away twelve apples!
STEP 11
So, gives us .
Then, gives us our **final answer**: .
STEP 12
The simplified expression is .
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