Question 272933: -3* square root of 2 over square root of 6
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! Hope this helps in detail steps!
√= Square root
~= if you see this(~) symbol it's also square root, lets hope we don't! ☺
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-3*√((((2)/(√(6)))))
Remove the parentheses around the expression (2)/(~(6)).
-3*√(((2)/(√(6))))
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 (√(6))/(√(6)).
-3*√(((2)/(√(6))*(√(6))/(√(6))))
To eliminate the radical from the denominator, multiply √(6) by √(6) to get 6.
-3*√(((2*√(6))/(6)))
Multiply 2 by ~(6) to get 2√(6).
-3*√(((2√(6))/(6)))
Reduce the expression (2√(6))/(6) by removing a factor of 2 from the numerator and denominator.
-3*√(((√(6))/(3)))
Multiply -3 by √(((~(6))/(3))) to get -3√(((√(6))/(3))).
-3√(((√(6))/(3)))
Split the fraction inside the radical into a separate radical expression in the numerator and the denominator. A fraction of roots is equivalent to a root of the fraction.
-(3√((√(6))))/(√(3))
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 will eliminate the radical in the denominator is (√(3))/(√(3)).
-(3√((√(6))))/(√(3))*(√(3))/(√(3))
Multiply the original expression by a factor of 1 ((√(3))/(√(3))) to eliminate the radical from the denominator.
(-3√((√(6)))*√(3))/(3)
Simplify the rationalized fraction.
-(3√(((√(6))(3))))/(3)
Reduce the expression -(3√(((√(6))(3))))/(3) by removing a factor of 3 from the numerator and denominator.
-√(((√(6))(3)))
Multiply √(6) by 3 to get 3√(6).
-√(((3√(6))))
Remove the parentheses around the expression 3√(6).
Answer: -√((3√(6)))
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