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Square Roots Videos 13 videos
Number Sense: Drill Set 5, Problem 5. Between which two integers does the square root of 80 lie?
Number Sense: Drill Set 6, Problem 2. The square root of 35 is between which of the following numbers?
ACT Math Intermediate Algebra Drill 2, Problem 2. How else can the expression be written?
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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