I have tried solving this problem over and over but I'm still not sure with my answer.
The question is sqrt2 / 2 + sqrt2.
I think the answer is 1/sqrt2 + sqrt2 because you have to cancel out the common factors.
Don't know what you want done with "solve"
We solve equations, but you don't have one.
Did you mean "evaluate" ?
Also , did you mean it the way you typed it, or did you mean
√2/(2+√2) ?
Back before we had calculators, it was often useful to have this rationalized, if so , then ...
= √2/(2+√2) * (2 - √2)/(2 - √2)
= (2√2 - 2)/(4-2)
= 2( √2 - 1)/2
= √2 - 1
you can usually check this kind of work by evaluating the original and the final answer on your calculator.
My answer is correct
Yes, sorry I meant evaluate. But the equation is not √2/(2+√2). The equation is √2/2 + √2
ok, that makes it easy
√2/2 + √2
= √2( 1/2 + 1)
= √2(3/2)
= 3√2/2
To solve the expression sqrt(2) / 2 + sqrt(2), we need to simplify it step by step.
Step 1: Combine like terms
The terms sqrt(2)/2 and sqrt(2) are not like terms. Like terms have the same radical and the same base, so they can be combined. In this case, sqrt(2)/2 represents a fraction, while sqrt(2) is just a radical.
Step 2: Rationalize the denominator
To simplify a fraction with a radical in the denominator, we need to rationalize the denominator. The term sqrt(2)/2 already has a rational denominator, so we don't need to rationalize it.
Step 3: Add the terms
Now, let's add sqrt(2)/2 + sqrt(2). To do this, we need a common denominator. The common denominator is 2, since 2 is a factor of 2.
sqrt(2)/2 + sqrt(2) = sqrt(2)/2 + (sqrt(2) * 2/2)
= sqrt(2)/2 + (2 * sqrt(2))/2
= (sqrt(2) + 2 * sqrt(2))/2
= (sqrt(2) + 2 * sqrt(2))/(2 * 1)
= (1 + 2) * sqrt(2)/2
= 3 * sqrt(2)/2
= 3/2 * sqrt(2)
So, the simplified answer to sqrt(2)/2 + sqrt(2) is 3/2 * sqrt(2).