Rationalize the denominator 5/√[3] + √[5]?

Question

How do you rationalize the denominator?

Answer 1

Is it:

5/[√3+√5]

Or:

[5/√3]+√5

Because according to the order of operations, it is the second one. However, i will do both.

5/(√3+√5)

To rationalize x/(√a+√b) multiply by (√a-√b)/(√a-√b) to get x(√a-√b)/(a-b)

So, set x=5, a=3, b=5 to get:

5(√3-√5)/(3-5)=(-5/2)(√3-√5) or (5/2)(√5-√3)

Or:

(5/√3)+√5=(5+√5√3)/√3=

(5+√15)/√3=((5+√15)√3)/3=

(5√3+√45)/3=

(5√3+3√5)/3=

(5/3)√3+(3/3)√5=

(5/3)√3+√5

HTH

peace

Answer 2

5/sqrt(3) + sqrt(5)

Multiply first term by sqrt(3)/sqrt(3) = 5 * sqrt(3) / 3

Multiply second term by 3 / 3

Add two terms.

Answer = (5 * sqrt (3) + 3 * sqrt(5)) / 3

Answer 3

Square roots cannot be in the denominator, so simply multiply the denominator to the numerator and have the base of the denominator be the new denominator. In other words: 5/√3 = (5√3)/3. So:

5√3 + √5

(5√3)/3 + √5