Question 213597: what is the answer to this problem? i have gotten stuck.
the square root of two thirds and the square root of three fourths.
sorry i forgot to say i needed it simplified.
studying for a chapter test tomorrow.
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! sqrt (2/3),,,,,,,sqrt (3/4)
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to simplify (reduce) we factor, but with perfect squares(1,4,9,16,25,36,49,etc)
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Let's do sqrt (3/4) first,,,
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This also equals ,,,,(sqrt 3)/ (sqrt 4),,,,
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the sqrt of 3 has only 1 as a potential factor, and this does not help
The sqrt of 4 has 4 as a perfect square (2*2), and can be simplified
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To (sqrt 3)/ (2),,, (just 2,, no sqrt),,,so
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sqrt(3/4) = (sqrt 3) /2 = (1/2) sqrt 3
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checking with a calc, sqrt(3/4) = .866,,,,1/2 sqrt3=.866,,,,ok
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Returning to sqrt(2/3), there are no perfect square factors that will help, so this is in simplified form already.
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sqrt(2/3) = sqrt .667 = .816
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a Better example might be sqrt50 = sqrt(25*2)= sqrt25 * sqrt2= 5sqrt2
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or sqrt 200 = sqrt(100*2) = sqrt(100) * sqrt2 = 10sqrt2
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