If square root of negative 1/4 = plus/minus half i. Does that mean that square root 4= +-2? whats the differ?

Question

If square root of negative 1/4 = plus/minus half i. Does that mean that square root four= +-2? whats the difference. I don't think square root 4=+-2 isn't square root 4=2 at least when i press the calculator.
Please explain and hopefully some examples too.

ok the main point is that usually when i do a sum x^2=4, i usually square root both sides to get x= +- square root 4 but in this case there is no -square root 4 but only square root 4.

Surely there should be some difference!!!

Answer 1

The calculator only shows what is called the PRINCIPAL square root, which is the positive one. This is because in a true sense, y = sqrt(x) is not a function.

So when you take the square root of both sides of an equation to try to solve it, you must always check both the positive answer and the negative.

Suppose (3-x)^2 = 4

If you square root both sides to get 3-x = 2, you will find the solution x = 1. But 5 is also a solution, as (3-5) = -2 and (-2) squared is 4. So you need to also look at the equation 3 - x = -2 to get this second answer.

Answer 2

I believe the focus of your question is on the +/- 2.
This simply means that both +2 and -2 when squared, give you +4. And of course, the imaginary 'i' is there because you cannot take the square root of a negative number.

If you were to plot the equation y = x^2 on graphic paper, you would get a parabola and 2 of the points on the parabola would be (2, 4) and (-2, 4). Any equation of the second degree (i.e. the highest exponent is 2) produces a parabola which confirms that for each value of y, there are 2 values of x; Except for the maximum or minimum point which is usually found by taking the derivative of the equation.

Answer 3

You get +/- 0.5i for √-1/4 because it's impossible to get the square root of a negative number. 'i' is a way to notate √-1 and even though you can't get the root of a negative, you might find the possibility of multiplying or powering it so that you get a real number. But if you multiply -2 x -2 you'll get 4. If you multiply 2 x 2 you'll also get 4. The square root of any real number will always have a positive and a negative number.

The difference between 4 and -1/4 is that negative sign before 1/4.

Answer 4

\/-1/4 = -1/2i or +1/2i because those answers are elements of complex numbers
For the integers numbers, negatives don't have roots. Only positive numbers have roots those: one is positive and another, negative. Example:
\/4 = -2 or +2 => To use one or other.
Justify:
For root -2 = -2*-2 = (-2)² = 4
For root +2= +2 *+2 = (+2)² = 4
\/-4 = There is no root as integers numbers.
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Answer 5

Yes. √4=+/-2
√-1/4=√-1*1/√4=+/-i*1/2=+/-i/2

Answer 6

Mathematically, the equation being quadratic has 2 roots -- even tho they need not be distinct --
x^2 = 4 has 2 possible solutions + - 2.

(x-2)^2 = 0 has 2 roots; they're both the number 2 -- example of the 2 roots not being distinct.

x^2 = 1 has 2 distinct roots: + - 1

Answer 7

the sqrt(-1/4) is not = +/- .5
cuz it has an imaginary root
it is =.5sqrt(-1)

Do not depend solely on ur calculator :
2^2 and (-2)^2 both =4
if x^2 =a^2 then always x=+/-a
but if it is given as a function f(x)=sqrtx then u take only the +ve roots
if u solve this equation :x^2 + x+1=0
the calculator will give u its roots even though the roots r imaginery and therefore the ans is not correct