Can someone please check my work on this problem? For some reason, I get the feeling that I did it wrong.
sqrt=square root (by the way)
3-sqrt10 sqrt5+sqrt2
-------- * ----------
sqrt5-sqrt2 sqrt5+sqrt2
(3-sqrt10)(sqrt5+sqrt2)
= -----------------------
5-2
3sqrt5+3sqrt2-sqrt50-sqrt20
--------------------------
3
Thanks in advance!
Yes, however, I would simplify
sqrt 12= 2 sqrt3
sqrt 50= 5sqrt2
sqrt 20= 2sqrt5
do that , and you can simplify more.
I don't think I have to know the sqrt12...?
So the answer would be -2sqrt2+1sqrt5
-------------- ?
3
To check your work, let's simplify the expression step by step:
First, let's multiply the numerators and denominators:
(3 - √10)(√5 + √2) = (3√5 + 3√2 - √10√5 - √10√2) / (√5 - √2)(√5 + √2)
Next, simplify the numerator by combining like terms.
Combining the like terms 3√5 and -√10√5, we get:
(3√5 - √10√5 + 3√2 - √10√2) / (√5 - √2)(√5 + √2)
Now, we can simplify further by simplifying the square roots:
√10√5 can be simplified as √(10*5) = √50 = 5√2,
and √10√2 can be simplified as √(10*2) = √20 = 2√5.
So now, the numerator simplifies to:
(3√5 - 5√2 + 3√2 - 2√5) / (√5 - √2)(√5 + √2)
Now, let's combine like terms again:
(3√5 - 2√5 + 3√2 - 5√2) / (√5 - √2)(√5 + √2)
Simplifying further, we get:
√5 + √2 / (√5 - √2)(√5 + √2)
Now, we can simplify the denominator by using the difference of squares formula:
(√5 - √2)(√5 + √2) = (√5)^2 - (√2)^2 = 5 - 2 = 3
So the final expression simplifies to:
(√5 + √2) / 3
Therefore, your expression is correct. It simplifies to (√5 + √2) / 3.
If you want to simplify it further, you can rationalize the denominator:
√5 + √2 / 3 can be written as (√5 + √2)(√3) / 3(√3) = (√15 + √6) / 3√3.