Posted by NEED HELP on Monday, September 29, 2014 at 9:12pm.
Have three problems and I'm really confused how to solve/simplify
1. 4/3+square root of 5
2. -4/-4+4square root of 2
3. 1/1+ square root of 2
1. did you mean
4/(3 + √5)
or
4/3 + √5 , the way you wrote it.
secondly, what do you want to "solve" ?
are you studying rationalizing the denominator?
My question also applies to the other two questions
recall that (a+b)(a-b) = a^2-b^2
so, (3+√5)(3-√5) = 9-5 = 4
So, to simplify such fractions, look for the "square conjugate" if you will, of the denominator.
4/(3+√5) = 4(3-√5) / (3+√5)(3-√5)
= 4(3-√5)/4 = 3-√5
And do the others the same way. You can check your answers at wolframalpha.com
For the first one, just enter
4/(3+√5)
in the box and it will show various data about the expression
http://www.wolframalpha.com/input/?i=4%2F%283%2B%E2%88%9A5%29
To solve or simplify the given expressions, let's break them down step by step.
1. 4/3 + square root of 5:
To simplify this expression, we need to find a common denominator. In this case, the common denominator is 3. So, multiplying the numerator and denominator of the first term (4/3) by 3, we get (4 * 3) / (3 * 3) = 12/9.
Now, we add this fraction (12/9) to the square root of 5. Since we cannot add a fraction and a square root directly, we need to rationalize the denominator.
To rationalize the denominator, we multiply the numerator and denominator of the square root of 5 by the conjugate of the denominator, which is (3 - square root of 5).
So, the expression becomes (12/9) + ((square root of 5 * (3 - square root of 5))) / (3 * (3 - square root of 5)).
Expanding and simplifying further, we get (12/9) + (3 * square root of 5 - 5) / (9 - 3 * square root of 5).
This expression is the simplified form of 4/3 + square root of 5.
2. -4/-4 + 4 * square root of 2:
To simplify this expression, we can start by simplifying the fractions separately.
The first fraction, -4/-4, simplifies to 1 (-4 divided by -4 equals 1).
Now, we have 1 + 4 * square root of 2.
This expression cannot be simplified further since the terms are not like terms.
So, the simplified form of -4/-4 + 4 * square root of 2 is 1 + 4 * square root of 2.
3. 1/1 + square root of 2:
To simplify this expression, we need to find a common denominator. In this case, the common denominator is 1. So, multiplying the numerator and denominator of the first term (1/1) by 1, we get (1 * 1) / (1 * 1) = 1/1, which is equal to 1.
Now, we add 1 to the square root of 2. This expression cannot be simplified further since the terms are not like terms.
So, the simplified form of 1/1 + square root of 2 is 1 + square root of 2.