How do I write this into SRform please walk me through
5/(sqrt5 - sqrt 3)
Rationalize the denominator by multilpling the numerator and denominator by (sqrt5+sqrt3).
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how come when I put into my calculator
(sqrt5 - sqrt 3)^2
i get .2540333076 not 5-3 or simply 2...?????????
(A-B)^2 = A^2 + B^2 - 2AB
So if you substitute A=sqrt5, and B=sqrt3, you get
(sqrt5-sqrt3)^2
=5+3-2*sqrt(15)
=8-2*sqrt(15)
=0.254...
I do see however when I put into my calculator
(5^(2^-1)-3^(2^-1))^-1(5^(2^-1)-3^(2^-1))^-1^-1 I get one in the denomenator which is not what I'm trying to do?
yah but i have to do it with out a calculator it's SRform right has to be done without calculator?
=0.254...
I see why I get this but I don't think I'm suppose to get an answer that has a lot of digits correct?
Did you read the short tutorial about rationlizing the denominator by muliplying by the conjugate? Do that.
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Thanks.
You did not follow Bob's suggestion. You should be multiplying sqrt5 - sqrt3 by sqrt5 + sqrt3 in the denominator.
Your answer will still have "a lot of digits" if done in decimal form because there will be a radical in the numerator. You should not be using a calculator for this question.
The answer is (5/2)(sqrt5 + sqrt3) = 9.92..
To write the expression 5/(sqrt 5 - sqrt 3) in a simplified form, we will employ a technique called rationalizing the denominator. The goal is to eliminate the square root terms from the denominator.
Step 1: Start by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of sqrt 5 - sqrt 3 is sqrt 5 + sqrt 3.
[ 5/(sqrt 5 - sqrt 3) ] * [ (sqrt 5 + sqrt 3)/(sqrt 5 + sqrt 3) ]
= [ 5(sqrt 5 + sqrt 3) ] / [ (sqrt 5 - sqrt 3)(sqrt 5 + sqrt 3) ]
Step 2: Now, we will simplify the denominator by applying the difference of squares formula. The difference of squares formula states that (a - b)(a + b) = a^2 - b^2.
= [ 5(sqrt 5 + sqrt 3) ] / [ (sqrt 5)^2 - (sqrt 3)^2 ]
= [ 5(sqrt 5 + sqrt 3) ] / [ 5 - 3 ]
= [ 5(sqrt 5 + sqrt 3) ] / 2
So, the simplified form of 5/(sqrt 5 - sqrt 3) is 5(sqrt 5 + sqrt 3)/2.