How is this possible?
Then what is √32 = ?
√8 = 2√2 ? why?
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Sqrt(8) = Sqrt(4*2)
Sqrt(4*2) = Sqrt(4) * Sqrt(2)
We know what the square root of 4 is: 2.
Thus, the square root of 8 simplifies to 2*sqrt(2)
For the square root of 32:
Sqrt(32) = Sqrt(16*2)
Sqrt(16*2) = Sqrt(16) * Sqrt(2)
4*Sqrt(2)
Sqrt(4*2) = Sqrt(4) * Sqrt(2)
We know what the square root of 4 is: 2.
Thus, the square root of 8 simplifies to 2*sqrt(2)
For the square root of 32:
Sqrt(32) = Sqrt(16*2)
Sqrt(16*2) = Sqrt(16) * Sqrt(2)
4*Sqrt(2)
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You can think of √ as this: You need two prime numbers inside the √ to take out and become one outside the √ sign.yumi2012 wrote:How is this possible?
Then what is √32 = ?
For example:
If you find all the prime numbers in 8 you get 2*2*2=8. So.. √2*2*2= 2√2 because you have 3 2's. You can take two 2's out to become one 2. But because you have 1 left over it must stay inside.
In √32 we get 2*2*2*2*2=32, so we have 5 2's. We can "take out" 4 2's (but remember you take out two becomes one) so... 2*2=4. We still have one left over inside so our answer is 4√2
Hope this helps
A useful website I found that has every quant OG video explanation:
https://www.beatthegmat.com/useful-websi ... tml#475231
https://www.beatthegmat.com/useful-websi ... tml#475231
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All of this uses a rule that says: sqrt(ab) = [sqrt(a)][sqrt(b)]
So, sqrt(32) = sqrt(16 x 2)
= sqrt(16) x sqrt(2)
= 4 x sqrt(2)
= 4sqrt(2)
Cheers,
Brent
So, sqrt(32) = sqrt(16 x 2)
= sqrt(16) x sqrt(2)
= 4 x sqrt(2)
= 4sqrt(2)
Cheers,
Brent