SOLUTION: Please show me how to do this. sqrt20/5 - 1/sqrt5 Only the 20 in the numerator is in the sqrt in the first half and only the 5 in the denominator is in the sqrt in the second

Algebra ->  Radicals -> SOLUTION: Please show me how to do this. sqrt20/5 - 1/sqrt5 Only the 20 in the numerator is in the sqrt in the first half and only the 5 in the denominator is in the sqrt in the second      Log On


   

Question 40617: Please show me how to do this.
sqrt20/5 - 1/sqrt5
Only the 20 in the numerator is in the sqrt in the first half and only the 5 in the denominator is in the sqrt in the second half.
Thanks
Found 3 solutions by junior403, josmiceli, gsmani_iyer:
Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2820%29%2F%285%29+-+%281%29%2Fsqrt%285%29
These problems can be a little tricky, but lets see if we I can help you.
First, we need to simplify these fractional expression individualy before we can work with them together.
Lets start with the first expression sqrt%2820%29%2F5%29, this can be simplified if we think of the numerator as sqrt%284%2A5%29%2F5.
We know that the 4 is a square of 2*2 so we can bring out the 2 so it looks like this...
2%2Asqrt%285%29%2F5%29
Thats all we can really do with the first expression, so lets move on to the next fraction -%281%29%2Fsqrt%285%29
This is a little different since we have a radical in the denominator instead of the numerator. The rule for radicals tells us that we need to rationalize this expression in order to eliminate the radical from any denominator.
To do that we need to multiply the entire fractional expression by the denominator, like so...
-%281%29%2Fsqrt%285%29%2Asqrt%285%29%2Fsqrt%285%29
What this does is it cancels out the square roots in the denominator because sqrt%285%29%2Asqrt%285%29 equals sqrt%285%5E2%29 which is 5.
The numerator now becomes -sqrt%285%29 so our entire problem now looks like this...
2sqrt%285%29%2F%285%29+-+sqrt%285%29%2F5
Are you with me so far...
Now we have an expression that can be more easily managed...
When subtracting rational expressions we treat them the same way we would any fractional expression.
2sqrt%285%29+-+sqrt%285%29 or 2sqrt%285%29+-+1sqrt%285%29 = sqrt%285%29
And when subtracting fractions we know that when we have to same denoninator (which we do) in two fractions we can simply write our answer containing the same denominator.
So our final equation and answer would be...
2sqrt%285%29%2F%285%29+-+sqrt%285%29%2F5+=+sqrt%285%29%2F5
I hope this helps.
Good Luck!






Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2820%29+%2F+5+-+1+%2F+sqrt%285%29
multiply top and bottom of 2nd fraction by sqrt%285%29
sqrt%2820%29+%2F+5+-+1%2Asqrt%285%29+%2F+%28sqrt%285%29%2Asqrt%285%29%29
sqrt%2820%29+%2F+5+-+sqrt%285%29+%2F+5
%28sqrt%2820%29+-+sqrt%285%29%29+%2F+5
%282%2Asqrt%285%29+-+sqrt%285%29%29+%2F+5
sqrt%285%29+%2F+5 answer

Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2820%29%2F5 - 1%2Fsqrt%285%29
= sqrt%2820%29%2F5 - sqrt%285%29%2F5 (By multiplying the second part by sqrt%285%29%2Fsqrt%285%29 so that the denominators will be same.)
= sqrt%284%2A5%29%2F5 - sqrt%285%29%2F5
= 2sqrt%285%29%2F5 - sqrt%285%29%2F5
= sqrt%285%29%2F5. Answer.
I think this is clear to you.
gsm