Question

rationalize4+√5/4-√5+ 4-√5/4+√5​

Answer 1

Answer:

8

Step-by-step explanation:

Rationalize the following:

4 + (sqrt(5))/4 - sqrt(5) + 4 - (sqrt(5))/4 + sqrt(5)

Put each term in 4 + (sqrt(5))/4 - sqrt(5) + 4 - (sqrt(5))/4 + sqrt(5) over the common denominator 4: 4 + (sqrt(5))/4 - sqrt(5) + 4 - (sqrt(5))/4 + sqrt(5) = 16/4 + (sqrt(5))/4 + (-4 sqrt(5))/4 + 16/4 + (-sqrt(5))/4 + (4 sqrt(5))/4:

16/4 + (sqrt(5))/4 + (-4 sqrt(5))/4 + 16/4 + (-sqrt(5))/4 + (4 sqrt(5))/4

16/4 + (sqrt(5))/4 - (4 sqrt(5))/4 + 16/4 - (sqrt(5))/4 + (4 sqrt(5))/4 = (16 + sqrt(5) - 4 sqrt(5) + 16 - sqrt(5) + 4 sqrt(5))/4:

(16 + sqrt(5) - 4 sqrt(5) + 16 - sqrt(5) + 4 sqrt(5))/4

16 + sqrt(5) - 4 sqrt(5) + 16 - sqrt(5) + 4 sqrt(5) = 32:

32/4

The gcd of 32 and 4 is 4, so 32/4 = (4×8)/(4×1) = 4/4×8 = 8:

Answer:

8

Answer 2

Here u go

Hope it helps u