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) About Me  (Show Source):
You can put this solution on YOUR website!
#1

sqrt%2850%29%2B2%2Asqrt%2832%29-sqrt%288%29 Start with the given expression


sqrt%2850%29%2B2%2Asqrt%2832%29-sqrt%288%29 Simplify sqrt%2850%29 to get 5%2Asqrt%282%29. Note: If you need help with simplifying the square root, check out this solver.



5%2Asqrt%282%29%2B2%2A4%2Asqrt%282%29-sqrt%288%29 Simplify sqrt%2832%29 to get 4%2Asqrt%282%29.


5%2Asqrt%282%29%2B2%2A4%2Asqrt%282%29-2%2Asqrt%282%29 Simplify sqrt%288%29 to get 2%2Asqrt%282%29.


5%2Asqrt%282%29%2B8%2Asqrt%282%29-2%2Asqrt%282%29 Multiply 2 and 4 to get 8


Since we have the common term sqrt%282%29, we can combine like terms


%285%2B8-2%29sqrt%282%29 Combine like terms. Remember, 5x%2B3x-4x=%285%2B3-4%29x=4x


11%2Asqrt%282%29


So sqrt%2850%29%2B2%2Asqrt%2832%29-sqrt%288%29 simplifies to 11%2Asqrt%282%29




#2




%282%29%2F%28sqrt%286%29-sqrt%285%29%29 Start with the given expression


Multiply by the fraction by %28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29%2Bsqrt%285%29%29. Note sqrt%286%29%2Bsqrt%285%29 is the conjugate of sqrt%286%29-sqrt%285%29.


Combine the fractions


Foil the denominator


Cancel like terms


%28%282%29%28sqrt%286%29%2Bsqrt%285%29%29%29%2F%286-5%29 Multiply

%28%282%29%28sqrt%286%29%2Bsqrt%285%29%29%29%2F%281%29 Combine like terms


%282%29%28sqrt%286%29%2Bsqrt%285%29%29 Remove the denominator of 1


2%2Asqrt%286%29%2B2%2Asqrt%285%29 Distribute

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1. Perform the indicated operations:
+sqrt%2850%29%2B+2sqrt+%2832%29-+sqrt+%288%29...........calculate each square root and substitute values
+%287.07%29+%2B+2%2A+%285.66%29-+%282.83%29+
+7.07+%2B+11.32+-+2.83+
+18.39+-+2.83+
+15.56...........your answer

2. Rationalize the denominator
2+%2F+%28sqrt%286%29-+sqrt+%285%29%29

2+%2F+%282.45+-+2.24%29

2+%2F+%280.21%29

9.5%29...................your answer





Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) Perform the indicated operations:
sqrt%2850%29%2B2sqrt%2832%29-sqrt%288%29
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.
sqrt%2850%29+=+sqrt%282%2A25%29 25 is a perfect square, 25+=+5%5E2 and sqrt%285%5E2%29+=+5, so...
sqrt%2850%29+=+sqrt%282%2A25%29=sqrt%282%29%2Asqrt%2825%29=sqrt%282%29%2A5 or 5%2Asqrt%282%29
Similarly for:
2%2Asqrt%2832%29+=+2%2Asqrt%282%2A16%29 = 2%2Asqrt%282%29%2Asqrt%2816%29+=+2%2Asqrt%282%29%2A4or 2%2A4%2Asqrt%282%29+=+8%2Asqrt%282%29
and for:
sqrt%288%29+=+sqrt%282%2A4%29=sqrt%282%29%2Asqrt%284%29+=+sqrt%282%29%2A2 or 2%2Asqrt%282%29
OK, now let's put all of this together:
sqrt%2850%29%2B2sqrt%2832%29-sqrt%288%29+=+5%2Asqrt%282%29%2B8%2Asqrt%282%29-2%2Asqrt%282%29 Now we can combine all of the sqrt%282%29's
5%2Asqrt%282%29%2B8%2Asqrt%282%29-2%2Asqrt%282%29+=+%285%2B8-2%29%2Asqrt%282%29=11sqrt%282%29
2) Rationalize the denominator:
2%2F%28sqrt%286%29-sqrt%285%29%29
To rationalize the denominator, you will multiply both the numerator and the denominator by the "conjugate" of the denominator sqrt%286%29-sqrt%285%29 and this is just sqrt%286%29%2Bsqrt%285%29
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 %28a-b%29%28a%2Bb%29+=+a%5E2-b%5E2
So after multiplying, as indicated, the denominator will look like:
%28sqrt%286%29%29%5E2+-+%28sqrt%285%29%29%5E2+=+6-5=1, so all we have left is the numerator:
2%2A%28sqrt%286%29%2Bsqrt%285%29%29