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ACT Math 2.3 Intermediate Algebra 322 Views


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Description:

ACT Math: Intermediate Algebra Drill 2, Problem 3. Which of the following is equal to the expression shown?

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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.

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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