Square root  2 + square root  2/9? Please explain how to obtain the answer of 4 square root of 2 over 3

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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`sqrt2 + sqrt(2/9)`

Simplify the second term which can also be written as `sqrt2/sqrt9`

We know that the `sqrt9=3` or -3 but we do not need the -3 for this particular answer so will only solve using `sqrt9=3`

So we now have

`sqrt2 +sqrt2/3` 

Now we need to find the common denominator (LCD) which is 3  So we multiply the first term by 3 in line with the LCD and as the second term already has the 3 we just leave as is or multiply by 1.

`sqrt2/1 times 3 +sqrt2/3 times 1`  


= `(3sqrt2 + sqrt2)/3`  

This can also be written as `(3sqrt2 +1sqrt2)/3`

Compare it to algebra. If it was 3x + x that would be 4x because we would add the two together. Apply the same principle to `3sqrt2 +1sqrt2`  Thus:

= `(4sqrt2)/3`


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