Question

rationalize the denominator​

Answer 1

Answer:

this is your answer I hope it will help you

Answer 2

Answer:

1). 4 + √11

2). 3 + 2√2

Solution:

Here,

The given Irrational numbers are :

5/(4 + √11) and (√2 - 1) / (√2 + 1) .

We need to simply the given Irrational numbers by rationalizing their denominators and further we need to find their conjugates .

Thus,

Here we go ↓

1). 5/(4 + √11)

→ 5/(4 + √11) = 5(4 - √11) / (4 + √11)(4 - √11)

= 5(4 - √11) / (4² - √11²)

= 5(4 - √11) / (16 - 11)

= 5(4 - √11) / 5

= 4 - √11

→ Conjugate = 4 + √11

2). (√2 - 1) / (√2 + 1)

→ (√2-1)/(√2+1) = (√2-1)(√2-1) / (√2+1)(√2-1)

= (√2 - 1)² / (√2² - 1²)

= (√2² + 1² - 2•√2•1) / (2 - 1)

= (2 + 1 - 2√2) / 1

= 3 - 2√2

→ Conjugate = 3 + 2√2