Help with eighth grade math!?

Question

let's say i have this problem:

5=x^2

when i cancel out the ^2 from x, i must square root 5.

but the answer turns out to be: plus or minus sqrt 5 = x

why does it have to be plus or minus?

when you square root both sides of the equation, does it always have a plus or minus sign?

Answer 1

Equations with an x^2 term have two answers.

Equations with an x^3 term have three answers.

etc.

Sometimes not all the answers are real, but when they are, the teacher will generally want to see both.

As you know, (-1)^2 = 1 and 1^2 =1

Similarly, sqrt(5)^2 = 5 and (-sqrt(5))^2 = 5

Answer 2

yes it must always be plus or minus but in the future both answers might not be used

when you square both sides again to get the original equation both negative and positive five works to get x^2 so both are the answer

Answer 3

the reason is simple. sqrt 5 * sqrt 5 = 5, and so is sqrt-5  * sqrt-5 = 5

because we are multiplying, the negative signs get canceled. There when you take a squareroot of 5 the answer could be positive or negative, but if its a root of -5, then the answer is sqrt-5.

Answer 4

Think about it this way:

x² = 36

x = ±6

Since multiplying two negatives together you get a positive, both of these are true:

6² = 36

(-6)² = 36

So that's why when you take the square root of both sides of an equation, it always results in ±.

So your:

x² = 5

becomes:

x = ±√5

Answer 5

there is always two square roots for any positive number... a negative square root and a positive square root.

Take 9 for example:

The square root of 9 is 3 because 3 * 3 = 9

But -3 is also the square root of 9 because -3 * -3 = 9 and when you multiply two negative numbers, you get a positive number.

So plus & minus means answers for both the positive and the negative square root.

Answer 6

it has a + or - because

x times x = x^2

2 times 2 = 2^2

-2 times -2 = -2^2

2^2=4 and -2^2=4

(-2) times (-2) = 4

if you dont use plus or minus you could lose a variable

Answer 7

Most of the time yes, because think about it: if you square a negative number, for example -2 you get a positive 4, no? and if you square the reciprocal of that, 2, you get 4 also. So writing it with the plus sign over negative next to the answer is just a easier way to write it. The longer way to write your answer would be (sqrt 5, - sqrt 5)

Answer 8

Depends, you have to switch the numbers around and see what you get.

an example

5 times 5 = 25,

-5 times -5 = 25 see its the same

by the way, what are you doing in school in the summer time?

shame shame.

Answer 9

yes it always does when you square root anything because anything squared is positive so your original number could have been either negative or positive and you dont know which one it is

for example:

2^2=4

but -2^2 also equals 4

so when you take the square root and dont write plus or minus, you are only getting one of the answers

Answer 10

because negative anything and positive anything square rooted always comes out positive.

-5x-5 =25 5x5=25

thus if you root 25, you have to consider the answer may be -5 or +5.

Answer 11

yes it does let me try to explain

(-2)^2 =4 and (2)^2 =4

so -2 and 2 squared both equal 4

it is the same thing for other numbers

hope i helped :)

Answer 12

its plus or minus.. because if you sqrt -5 it equals 25 and if you square +5 it equals 25.. so it could be both possiblities.. its plus or minus when the exponent is even i believe.. but if its odd like 3 it can only have one possiblity.. i may be wrong.. school hasn't started yet so my brain is still off a bit lol

Answer 13

it must be plus or minus because look:

5 times 5 = 25, and

-5 times -5 = 25 also!