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Question 59007: what number is larger: sq rt of 7 + sq rt of 10 or sq rt of 3 + sq rt of 19?
I just dont undertand this problem. I know you are supposed to factor if number is not a perfect sqaure but these are prime numbers. help me please!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what number is larger: sq rt of 7 + sq rt of 10 or sq rt of 3 + sq rt of 19?
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Since we don't know how they are related we'll use "R" instead of =,>, or <.
sqrt7+sqrt10 R sqrt3+sqrt19
Square both sides to get:
17+2sqrt(70) R 22+sqrt(57)
2sqrt70 R 5+sqrt57
sqrt70 - sqrt57 R (5/2)
Square again to get:
13-2sqrt(70*57) R 25/4
27/4 R 2sqrt(3990)
27/8 R sqrt(3990)
Square again to get:
729/64 R 3990
Now we see that R is <
So sqrt7+sqrt10 is less than sqrt3 + sqrt19
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Using a calculator you get
The left side is 5.8080...
The right side is 6.0909...
So we were right: R is <
Cheers,
Stan H.
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