SOLUTION: There are two problems that i have submitted and i do not understand the answer can you explain how to do these two problems to me.
1. Perform the indicated operations:
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Question 118008: There are two problems that i have submitted and i do not understand the answer can you explain how to do these two problems to me.
1. Perform the indicated operations:
sqrt[50] + 2sqrt [32] - sqrt [8]
and the second one is
2. Rationalize the denominator
2 / sqrt[6] - sqrt [5]
thank you i really appreciate this i really do not understand this and the two tutors got these answers
julie
Found 3 solutions by jim_thompson5910, MathLover1, Earlsdon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1
Start with the given expression
Simplify to get . Note: If you need help with simplifying the square root, check out this solver.
Simplify to get .
Simplify to get .
Multiply 2 and 4 to get 8
Since we have the common term , we can combine like terms
Combine like terms. Remember,
So simplifies to
#2
Start with the given expression
Multiply by the fraction by . Note is the conjugate of .
Combine the fractions
Foil the denominator
Cancel like terms
Multiply
Combine like terms
Remove the denominator of 1
Distribute
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
1. Perform the indicated operations:
...........calculate each square root and substitute values
...........your answer
2. Rationalize the denominator
...................your answer
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) Perform the indicated operations:
The key here is to factor the integers under the radical (the radicands) and see if you have any perfect squares that can be taken outside the radical by taking the square root.
25 is a perfect square, and , so...
== or
Similarly for:
= or
and for:
= or
OK, now let's put all of this together:
Now we can combine all of the 's
=
2) Rationalize the denominator:
To rationalize the denominator, you will multiply both the numerator and the denominator by the "conjugate" of the denominator and this is just
The conjugate of (a+b) is (a-b) and the conjugate of (a-b) is (a+b), see the idea?
Let's look at the denominator which is in the form of
So after multiplying, as indicated, the denominator will look like:
=, so all we have left is the numerator:
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