What is the smallest integer greater than ?
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Is there a trick to this other than estimating the roots? I know √5≈2.236 and √3≈1.732 but adding them up and then figuring out the smallest integer greater feels like I could easily mess up the boundaries.
Same. I keep second-guessing whether it's just asking for the next integer or if I need to be more precise because the sum might be really close to an integer.
The trap is assuming the sum is close enough to an integer that rounding works. Check how close it actually is before picking.
This one is more about knowing a useful algebraic identity than about decimal approximations. If you square 5+√5+√3, you get an integer plus a radical piece, and then you can compare that radical piece to nearby perfect squares.
Right, that's the clean way. Estimating radicals to three decimals works, but squaring lets you prove which integer it's between without trusting your memory of √15.
I hate these "smallest integer greater than" questions because if the value is just barely above an integer, estimation to two decimals can fool you. How careful do I need to be on the actual GMAT?
Usually they design it so a reasonable estimate is enough, but for a 655-705 level question they may put the sum near a boundary. I'd verify with squares if it looks close.
Not sure why E is even there. If you approximate √5≈2.24 and √3≈1.73, the sum is about 8.97, so 5 plus that is around 13.97. That screams just under 14, which makes the answer feel obvious, but I've seen people pick 14 because they round too early.
Exactly, the whole question hinges on whether it's below or above 14, and 13.97 is suspiciously close. That's why I don't trust decimal approximations here.
What it tests
Your handling of square and higher roots, including simplifying radicals.
Common trap
Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.