How is 3/sqrt 3 = sqrt 3?

Question

How is 3/sqrt 3 = sqrt 3?

Answer 1

Here's a simpler way to look at it:

The square root of a number is another number which when multiplied by itself gives the first number.  For instance, the square root of 4 is 2 because 2 * 2 = 4; the square root of 25 is 5 because 5 * 5 = 25.  Using these two examples, it's easy to see that 4/sqrt 4 = sqrt 4 (4/2 = 2) and 25/sqrt 25 = sqrt 25 (25/5 = 5).  Following the pattern, 3/sqrt 3 = sqrt 3, because sqrt 3 * sqrt 3 = 3 (this is the rationalization the other answer mentioned).

The first answer, to rationalize both sides of the equation, is the correct technical answer, and is the only acceptable answer if asked to justify the truth of the equation.  When people see "sqrt", they tend to freak out and forget that the rules still apply; substituting whole numbers sometimes helps to see the truth of a situation.

Answer 2

3/sqrt(3) = 3/sqrt(3)*sqrt(3)/sqrt(3) = 3*sqrt(3) / 3 = sqrt(3)

you rationalize the denominator and it works out by canceling.  

Answer 3

3/sqrt 3 = sqrt 3

since sqrt 3 * sqrt 3 = 3

taking sqrt 3 (which is in the denominator) to the other side so that it gets multiplied.

3 = 3

therefore, the equation is true

Answer 4

You must know:

1. This is a problem to be solved by rationalizing.

2. 3 = sqrt 3 * sqrt 3  (This goes for any whole number)

Now we have,

   3 / sqrt 3    

        

= (sqrt 3 * sqrt 3) / sqrt 3

=   sqrt 3    (cancelling sqrt 3 of numerator and denominator)

There you go. Two simple steps. (write on a notebook, it will seem better)

          OR

You can multiply the numerator and the denominator by sqrt 3. Then in the denominator you will have:  sqrt 3 * sqrt 3        which is equal to 3. So cancelling the numerator and the denominator, you will get the answer.

Good Luck my friend

Answer 5

Alex, cross multiply ans verify! what's the matter>

Answer 6

3/sqrt(3)=3^(2/2)x3^(-1/2)  (same base)

               =3^(1/2)

                =sqrt(3)

Magic!!!!!

Answer 7

3/sqrt(3)= sqrt(3)

cause

3^1*3^(-1/2)= 3^(1/2)

3^(1/2) is equal to sqrt(3)

Basically when you have a square root on bottom, bring it up by giving it a negative power... 3^(-1/2)... then just simplify the rest!

OR

because 3=sqrt(3)*sqrt(3)

[SQRT(3)*SQRT(3)]/(SQRT(3))=SQRT(3)

3 is equal to square root of 3 times the square root of 3.

when you divide that by the square root of 3 it cancels out and you get the square root of three

sorry its kinda hard to follow cause i cant write anything out