SOLUTION: Rationalize the denominator and simplify 2/5sqrt 2

Question 388976: Rationalize the denominator and simplify
2/5sqrt 2
Found 3 solutions by haileytucki, stanbon, richard1234:
Answer by haileytucki(390)   (Show Source): You can put this solution on YOUR website!
(2)/(5~(2))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is (~(2))/(~(2)).
(2)/(5~(2))*(~(2))/(~(2))
To eliminate the radical from the denominator, multiply ~(2) by ~(2) to get 2.
(2*~(2))/(5*2)
Multiply 2 by ~(2) to get 2~(2).
(2~(2))/(5*2)
Multiply 5 by 2 to get 10.
(2~(2))/(10)
Reduce the expression (2~(2))/(10) by removing a factor of 2 from the numerator and denominator.
(~(2))/(5)
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Rationalize the denominator and simplify
2/5sqrt(2)
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Multiply numerator and denominator by sqrt(2) to get:
(2sqrt(2))/(5*2)
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= (1/5)sqrt(2)
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Cheers,
Stan H.
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Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
We have Multiplying both top and bottom by this becomes

which is equal to
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