Rationalize the denominator and simplify.
sqrt(6)/4srqrt(3) + sqrt(2) =
I cannot figure out how to do this and simplify. Can someone help me.
Thanks.
To rationalize the denominator and simplify the given expression, we need to get rid of the radical in the denominator.
First, let's simplify the expression:
sqrt(6) / (4 * sqrt(3)) + sqrt(2)
To start rationalizing the denominator, we'll rationalize the first term: sqrt(6) / (4 * sqrt(3)).
To rationalize this term, multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt(3):
(sqrt(6) / (4 * sqrt(3))) * (sqrt(3) / sqrt(3))
This gives us:
(sqrt(6) * sqrt(3)) / (4 * sqrt(3) * sqrt(3))
= (sqrt(18)) / (4 * 3)
= (sqrt(9) * sqrt(2)) / 12
= (3 * sqrt(2)) / 12
= (sqrt(2)) / 4
Now, let's simplify the second term: sqrt(2).
Finally, we can combine the simplified terms:
(sqrt(2))/4 + sqrt(2)
= (sqrt(2))/4 + (sqrt(2))/(1)
= (sqrt(2))/4 + (sqrt(2))/(4)
= (sqrt(2) + sqrt(2))/(4)
= (2sqrt(2))/(4)
= sqrt(2)/2
Therefore, the simplified expression is sqrt(2)/2.