SOLUTION: okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do a

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Question 171503: okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do after that or how to write it!
Found 4 solutions by stanbon, jim_thompson5910, Mathtut, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how do i simplify the square root of 128
The prime number breakdown of 128 is
128 = 2*64
= 2*2*32*
= 2*2*2*16
= 2*2*2*2*8
---
---
= 2*^7
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So sqrt(128) = sqrt(2^7)
= sqrt(2*6)*sqrt(2)
= 2*^3*sqrt(2)
= 8sqrt(2)
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A shorter way to go is
sqrt(64*2) = sqrt(64)*sqrt(2)
= 8*sqrt(2)
================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28128%29 Start with the given expression



The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers.


One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 128


Factors:
1, 2, 4, 8, 16, 32, 64, 128


Notice how 64 is the largest perfect square, so lets factor 128 into 64*2


sqrt%2864%2A2%29 Factor 128 into 64*2



sqrt%2864%29%2Asqrt%282%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



8%2Asqrt%282%29 Take the square root of the perfect square 64 to get 8



So the expression sqrt%28128%29 simplifies to 8%2Asqrt%282%29

----------------------------
Check:


Notice if we evaluate the square root of 128 with a calculator we get


sqrt%28128%29=11.3137084989848


and if we evaluate 8%2Asqrt%282%29 we get


8%2Asqrt%282%29=11.3137084989848


This shows that sqrt%28128%29=8%2Asqrt%282%29. So this verifies our answer

Answer by Mathtut(3670) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do after that or how to write it!
-------------------
sqrt%28128%29
=sqrt%2864%2A2%29
=sqrt%2864%29%2Asqrt%282%29
=8sqrt%282%29
The object of the game is to make the number under the radical as small as possible.