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Description:
Algebra and Functions: Drill Set 3, Problem 3. What is this expression equal to?
Transcript
- 00:05
And here's your shmoop du jour.
- 00:07
The expression... the square root of 64 x to the 8th times y to the 4th times z squared...
- 00:12
is equal to... what?
- 00:16
And here are the potential answers...
- 00:17
Before we spoil the ending, hit pause right now and solve it yourself.
Full Transcript
- 00:24
OK, this question is testing our basic ability to root.
- 00:27
Uh, no, this kind of root. Square kinds.
- 00:30
And it really tests one thing -- whether we realize that when exponents
- 00:34
are squared rooted, they are halved.
- 00:37
That is, the square root of x to the 100th power is x to the 50th power.
- 00:42
We can rewrite our original equation this way:
- 00:46
Hopefully we know right off the bat that the square root of 64 is 8.
- 00:50
And note that immediately we can cross off C and D as choices in the answer set.
- 00:54
Nice. We've got our chances down to a nice, manageable 50-50 shot here.
- 00:59
So then we take the square root of x to the 8th and we get x to the 4th...
- 01:03
y to the 4th becomes y squared and z squared becomes just z.
- 01:07
And the answer is A. Done. Go team.
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