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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?
CAHSEE Math 3.5 Algebra and Functions 272 Views
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Description:
Algebra and Functions: Drill Set 3, Problem 5. Simplify the expression.
Transcript
- 00:03
And here's your shmoop du jour.
- 00:07
Simplify 5a to the 8th times the square root of b to the 10th...
- 00:12
times 2 times the square root of a to the 8th times b to the 10th.
- 00:18
Here are the potential answers...
- 00:20
Before we spoil the ending, hit pause and try to solve this baby yourself.
Full Transcript
- 00:26
The trickiest part of this expression is recognizing that when we square root a variable with an exponent...
- 00:33
...the square root has the effect of dividing the exponent in half.
- 00:38
So the square root of b to the 10th becomes b to the 5th, and the square root of a to
- 00:44
the 8th becomes a to the 4th. The product of the coefficients 5 and 2 is
- 00:49
just 5 times 2, or 10.
- 00:51
The second important thing we need to know is that when we multiply monomials with the
- 00:56
same base, we can just add the exponents.
- 01:01
If we group like terms together, the product of the problem is 10 times a to the 8th times
- 01:06
a to the 4th... times b to the 5th times b to the 10th.
- 01:09
8 plus 4 equals 12, and 5 plus 10 equals 15...
- 01:13
...so we have 10 times a to the 12th power time b to the 15th....
- 01:18
...which gives us C.
- 01:20
The greatest thing about performing this mathematical trick is that...
- 01:23
...you can try this one at home.
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