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Intermediate Algebra Videos 25 videos
ACT Math Intermediate Algebra Drill 1, Problem 1. What is the product of (a – 3)2?
ACT Math Intermediate Algebra Drill 1, Problem 2. Find the product of (2a + 6)2.
ACT Math Intermediate Algebra Drill 1, Problem 4. Solve for x based on the equation.
ACT Math 2.3 Intermediate Algebra 321 Views
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Description:
ACT Math: Intermediate Algebra Drill 2, Problem 3. Which of the following is equal to the expression shown?
Transcript
- 00:02
Here's another shmoop du jour..
- 00:04
Which of the following is equal to the root
- 00:06
3 minus 1 over root 3 plus root 5? And here are your potential answers...
- 00:14
Okay, any time we get one of these, it's a good bet that we want to multiply by some
- 00:18
combination of the denominator to hopefully just simplify it.
Full Transcript
- 00:22
So in this case - we want a perfect square that's in the form of (a +b) times (a - b)...
- 00:26
Since we have the square root of 3 plus the square root of 5 on the bottom...
- 00:30
we have to multiply the fraction
- 00:31
by root 3 minus root 5 times over root 3 minus root 5...which is the equivalent of 1.
- 00:39
Based on the perfect square formula... with a equaling root 3 and b equaling
- 00:44
root 5...we have the bottom of the fraction simplifying to 3 minus 5...or negative 2.
- 00:50
We can use simple distribution properties for the top of the fraction.
- 00:54
Root 3 times root 3 equals 3. Root 3 times negative root 5 equals negative root 15...negative
- 01:02
1 times root 3 equals negative root 3...and negative 1 times negative root 5 equals positive root 5.
- 01:12
All over NEGATIVE 2.
- 01:14
But looking at our answer choices...none of them have a negative 2 at the bottom.
- 01:17
So let's just move it to the top. Keep in mind that we have to take the negative of
- 01:21
the ENTIRE top of the fraction...so we have to distribute a negative to each number...
- 01:27
Negative 3 plus root 15 plus root 3 minus root 5--all over 2.
- 01:32
Looks like answer choice E is the right one.
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