Question

solve:
sqrt(x)+7=3
x=

Answer 1

x = 16

Answer 2

sqrt(x)+7=3

sqrt(x)=3-7

sqrt(x)=-4

So there are no solutions since the range of the square root is nonnegative.

Answer 3

but all you have to do is square both sides to get x !

Answer 4

yes, but if x=16, then it doesn't satisfy the original equation. So there are no solutions.

Answer 5

thenn, idk.

Answer 6

yes no solutions its a trick question

Answer 7

check:


sqrt(x)+7=3



sqrt(16)+7=3



4+7=3 .... Note: NOT -4


11 = 3 ... this is NOT true, so there are NO solutions.

Answer 8

but squareroot x is
±x

i mean squareroot 16 can be +4 AND -4. thats how we solve all quadratic equations, remember?

Answer 9

ah good point, but the plus/minus only comes up when solving quadratics (equations like x^2=4)

The square root alone is just a function: one number in ----> one number out. The square root of 16 is 4 (not -4 at the same time)

Answer 10

really?? i had no idea :P now i just feel really stupid X_X

Answer 11

Thompson is right look at the graph of square root.

Answer 12

don't be, they push this plus/minus stuff all the time when it comes to square roots and I was confused about it before too

Answer 13

if you ask for the square root of 16 you get -4 and 4...but if you ask for \[\sqrt{16}\] then you only get 4. the notation \[\sqrt{}\] refers to the principal value of the square root....which is the unique positive number

Answer 14

oh, so you have to put the plus-minus sign before it to show it can be both, right?

Answer 15

Yes, if you want to show that it's both, then you put \[\large \pm\sqrt{16}\]

Answer 16

only if you ask for the square root and you don't use the notation or specifically ask for the principal value