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) (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
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= 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) (Show Source): You can put this solution on YOUR website!
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
Factor 128 into 64*2
Break up the square roots using the identity
Take the square root of the perfect square 64 to get 8
So the expression simplifies to
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Check:
Notice if we evaluate the square root of 128 with a calculator we get
and if we evaluate we get
This shows that . So this verifies our answer
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
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Answer by Alan3354(69443) (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!
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The object of the game is to make the number under the radical as small as possible.
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