why square roots are dumb

[charcot bouchard]

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I am hoping someone can tell me how the actual DAT defines square roots.

DAT Bootcamp has some contradictory problems. For example: one problem they ask you to solve for x when x^2 = 9. The correct solution is +/- 3. However, on a later problem, you solve for x when: x+2 = sqrt(5x+16). After factoring you get: (x-4)(x+3), leading you to believe that your solution set would be 4 and -3. However, Bootcamp says the correct answer is 4. -3 is incorrect because, by the DATs definition, square roots only yield positive values and plugging -3 into the left side of the equation would suggest that the square root on the right side of the equation yielded a negative value.

So... How does the ACTUAL DAT define square roots? Which of the above Bootcamp examples is correct? If you could respond urgently that would be appreciated as my DAT is tomorrow. Thanks!

 

[davdango]

I don't think it was a toss up between two answers for me for any problem. It would just be one of the answers they provide you, otherwise it would be too tricky. Good luck!

 

[pookatooth]

I am hoping someone can tell me how the actual DAT defines square roots.

DAT Bootcamp has some contradictory problems. For example: one problem they ask you to solve for x when x^2 = 9. The correct solution is +/- 3. However, on a later problem, you solve for x when: x+2 = sqrt(5x+16). After factoring you get: (x-4)(x+3), leading you to believe that your solution set would be 4 and -3. However, Bootcamp says the correct answer is 4. -3 is incorrect because, by the DATs definition, square roots only yield positive values and plugging -3 into the left side of the equation would suggest that the square root on the right side of the equation yielded a negative value.

So... How does the ACTUAL DAT define square roots? Which of the above Bootcamp examples is correct? If you could respond urgently that would be appreciated as my DAT is tomorrow. Thanks!

So (-3)^2 = 9. So is (3)^2. But square root of 1 (which you get when you plug in -3 into right side of equation) does not equal -1 (which you get when you plug in -3 to left side). Square rooting both sides of the equation to solve for x is different than squaring both sides of the equation. Always check back to the original equation to see if the methods you used to make it seem easier actually work in the original equation.