(2^0.5 + 5^0.5)^2
a) 7
b) 10
c) 13
d) 15
e) 17
Who knows a good way to solve this?
I did it like this, but I think there could be quicker ways:
1. step: 2^0.5 = 1.41 (everybody should know that without calculation)
2. step: 5^0.5 = approximately 2.2 (just by "guessing")
3. step: (1.41 + 2.2) = 3.6
4. step: 3.6^2 = 12.96 (calculation) --> so go with c)
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clock60
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hi friend
it is a very strange problem. we are not asked to give closest answer, so i need to practice several times harder to know the exact value of 10^1/2
(2^1/2+5^1/2)^2=2+2*(2*5)^1/2+7=7+2*(10)^1/2
9^1/2<10^1/2<16^1/2
3<10^1/2<4, so the value of 10^1/2 is somewhere between 3 and 4 closer to 3 say 3,4- closest rounding to 3
7+2*3=7+6=13
it is a very strange problem. we are not asked to give closest answer, so i need to practice several times harder to know the exact value of 10^1/2
(2^1/2+5^1/2)^2=2+2*(2*5)^1/2+7=7+2*(10)^1/2
9^1/2<10^1/2<16^1/2
3<10^1/2<4, so the value of 10^1/2 is somewhere between 3 and 4 closer to 3 say 3,4- closest rounding to 3
7+2*3=7+6=13
