Question 356972: Multiply. Assume variables represent nonnegative real numbers
1. sqrt(3)*(2sqrt(15)-3sqrt(4))
2. (3+sqrt(11))*(3-sqrt(11))
3. (sqrt(5)-sqrt(3))^2 Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! 1.
Since , we can start by substituting:
or
Now we can multiply, using the Distributive Property:
In the first product we use the property of radicals, , to multiply the two square roots. In the second factor we just use the Commutative Property to move the 6 in front:
We cannot subtract these two terms because they are not like terms. But we can simplify the first square root. (It has a perfect square factor: 9)
Using the same property of radicals as above (only "in reverse") we can split these two square roots:
Since :
or
2.
We can use FOIL to multiply this. Or we can take advantage of the difference of squares pattern, , with "a" being 3 and "b" being :
9 - 11
-2
3.
For this we can use FOIL. Or we can use a pattern, with "a" being and "b" being :
Note: Even if you use FOIL on #2 and #3, you still end up with the same answers as we did using patterns.
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