How can you de-rationalise the denominator of 3sqrt2/2?

In summary, to get 3/sqrt2 from 3sqrt2/2, you can use the property of (\sqrt{x})^2 = x to rationalize the denominator by multiplying both the numerator and denominator by \sqrt{2}. This will result in 3/sqrt2.
  • #1
Ry122
565
2
How do you get 3/sqrt2 from 3sqrt2/2?
 
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  • #2
Ask yourself what's (sqrt x)^2?
 
  • #3
hint: sqrt2/sqrt2 = 1
 
  • #4
sorry don't follow
 
  • #5
Try going the other way.
Start with
[tex] \frac 3 {\sqrt 2} [/tex]

to get

[tex] \frac {3 \sqrt 2} 2 [/tex]
 
  • #6
If you're going from 3sqrt2/2 to 3/sqrt2 you're basically de-rationalizing the denominator.
 
  • #7
By definition [itex](\sqrt{2})^2= \sqrt{2}\sqrt{2}= 2[/itex]. That means that
[tex]\frac{\sqrt{2}}{2}= \frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]
 
  • #8
Ry122 said:
How do you get 3/sqrt2 from 3sqrt2/2?

[itex]\frac{3}{\sqrt 2} . \frac{\sqrt 2}{\sqrt 2} = \frac{3 \sqrt 2}{2}[/itex].

This is rationalising the denominator as you cannot have a surd on the denominator. The question that you are asking is how you get the reverse, de-rationalising the denominator. Try opposite steps to the one I shown.
 

1. What is a square root?

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 x 5 = 25.

2. How do you find the square root of a number?

The most common method for finding the square root of a number is by using a calculator. However, you can also use a mathematical process called "long division" or an estimation method called "guess and check."

3. What is the difference between a perfect square and a non-perfect square?

A perfect square is a number that has an integer as its square root, such as 25, 36, or 49. A non-perfect square is a number that does not have an integer as its square root, such as 20, 30, or 50.

4. Can fractions have square roots?

Yes, fractions can have square roots. For example, the square root of 1/4 is 1/2, and the square root of 9/16 is 3/4.

5. How do you simplify a square root fraction?

To simplify a square root fraction, you need to find a perfect square that is a factor of both the numerator and the denominator. Then, you can divide both the numerator and denominator by that perfect square. For example, to simplify the fraction √12/√18, you can rewrite it as √(4x3)/√(9x2). Since 4 and 9 are both perfect squares, you can simplify further to get (√4x√3)/(√9x√2), which becomes 2√3/3√2.

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