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

Algebra ->  Algebra  -> Square-cubic-other-roots -> 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      Log On

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 Click here to see ALL problems on Square-cubic-other-roots 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(57387)   (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.