multiplying square roots

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Eva Barragan

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Feb 8, 2006
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the derictions are simplify. assume variables are nonnegative.
the problem is (sqaure root) (y-3)^6
the awnser i got was y^3-3^3
i got this awnser because i think that when the exponent is outside the equation isnt it talking about both y and 3?
well anyways i simplified it and got the awnser above
i feel i got this awnser totally wrong if i did can u help me figure out the awnser
thanx :)
 
Not quite:

sqrt[(y - 3)^6]
= [(y - 3)^6]^(1/2)
= (y - 3)^3
 
thanx for helping me :D
i think i get it now.
so i'm only supposed to simplify the exponent
you know divide it by the half power
 
did i do this problem right?
th derictions are: Multiply and Simplify. Assume variables are nonnegattive.
the problem is: sqrt[6/5] times sqrt[5/216]=sqrt[1/36]=1/6
i think thats right :?:
 
Eva Barragan said:
thanx for helping me :D
i think i get it now.
so i'm only supposed to simplify the exponent
you know divide it by the half power
Click to expand...

Not quite; (a^x)^y = a^(x * y)

(a^6)^(1/2) = a^(6 * 1/2) = a^3 (only looks like a division)

(a^6)^(3/2) = a^(6 * 3/2) = a^9 : clear ?
 
Eva Barragan said:
did i do this problem right?
th derictions are: Multiply and Simplify. Assume variables are nonnegattive.
the problem is: sqrt[6/5] times sqrt[5/216]=sqrt[1/36]=1/6
i think thats right :?:
Click to expand...
Correct.
You can check those yourself:
get the square root of 6/5
get the square root of 5/216
multiply the results: is the result = 1/6?
 
sqrt[(y - 3)^6] = [(y - 3)^6]^(1/2) = (y - 3)^3
Click to expand...
Except that is correct ONLY for y >= 3.

[(y - 3)^6]^(1/2) = |(y - 3)^3|.
 
It is a common error.

If one DOES NOT KNOW that x >= 0, this is mandatory:
\(\displaystyle \sqrt{x^{2}} = |x|\)

If one DOES KNOW that x >= 0, this is OK:
\(\displaystyle \sqrt{x^{2}} = x\)

That is why
\(\displaystyle \sqrt{64} = 8\)

But
\(\displaystyle \sqrt{(x-2)^{2}} = |x-2|\), NOT just x-2.

Do you know that (y-3)^3 >= 0?
 
You haven't answered my question.

You have this, "assume variables are nonnegative", from the problem statement. This tells us that y >= 0. What does that say about "y-3"? "(y-3)^3"?
 
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