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# GMAT: Math 25

129-132, pgs. 169-170. Created by Sal Khan.

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• For #130, I need someone to explain to me in a different way why choice E, |x - -1| is <= 4, is the correct answer. The video begins around . More specifically, why does Hal use a negative minus 1 which turns into a plus positive 1? • I don't have the printed material to refer to so just going by the video.
This refers to the Modulus of a number. Look up Modulus on the internet. It refers to an unsigned number or a number separate from its (+) or (-) signature.
Now (-) x (-) gives you a (+) so that takes care of the x+1
The Modulus |x+1| is now less than or equal to 4 because at this point we are only talking about an absolute value of x and disregarding its positive or negative signature.
• Q 129: In the 11th edition book, the answer uses 284 and 11.4. I can't understand why. Does it have something to do with that fact you stated that it never approaches 11.5 and it's always 11.4999..?
(1 vote) • At In Q 130 , why do we take midpoint i.e -1 and secondly why do we subtract -1 from it?
(1 vote) • Wait so it this kind of like percents?
(1 vote) • what is the square root of 20x to the 6 power over 25 to the simplest form
(1 vote) • hmm, so you mean √((20x⁶)/25) ? or do you mean (√(20x⁶)/25) ?
for √((20x⁶)/25)
Let's use this handy equivalent rule: √(A/B) = √A/ √B
√((20x⁶)/25) = √(20x⁶)/ `(√25)` = √(20x⁶)/` 5 `
Now we can use this other handy equivalent rule: √AC = √A ∙ √C
so, √(20x⁶) =√20 ∙ √x⁶
The square root of a power (base with an exponent) is going to be that exponent divided by 2 . Because x³ ∙ x³ = x⁶, then √x⁶ = x³

Making progress!
What we have left is (x³ ∙ √20)/5
All we need is √20)
For that we will use √DE = √D ∙ √E
√20 = √(4 ∙ 5) = √4 ∙ √5 = 2√5
At last, putting them all together:
√((20x⁶)/25) = 2/5 x³√5
Likewise, if you meant
(√(20x⁶)/25)