SOLUTION: 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 sqa

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?
--------
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
-----------
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.

RELATED QUESTIONS
what number is larger: a) sq rt of 7 or cube rt of 19. b) cube rt of 4 or 4th rt of 6. i... (answered by stanbon)

Sq rt of... (answered by fcabanski)

How would I rationalize the denominator of 1/sq rt 8-sq rt... (answered by josgarithmetic)

10*sq rt 7 + 8*sq rt 7 =... (answered by tutorcecilia)

Grade the following problem:; Perform the indicated operations: √[50] +... (answered by checkley77)

Given: S is the midpoint of RT. ST = SQ Prove: RT = SQ... (answered by richard1234)

I need to find the perimeter of a triangle. the long side of the triangle illustrates... (answered by Flake)

7 sq rt 100 _____________ (divided by) sq rt 500 Do I multiply both sides by sq rt (answered by jim_thompson5910)

what is the graph of x = -4(sq rt... (answered by Alan3354)