Question

rational the denominator 2 by √5-√3 and √3-1 by √3+1​

Answer 1

Answer:

1). √5 + √3

2). 2 - √3

Solution:

Here,

The given Irrational numbers are 2/(√5 - √3) and (√3 - 1)/(√3 + 1) .

We need to rationalise the denominators of the given Irrational numbers .

Thus,

Here we go ↓

1). 2/(√5 - √3)

2/(√5-√3) = 2(√5+√3) / (√5-√3)(√5+√3)

= 2(√5 + √3) / (√5² - √3²)

= 2(√5 + √3) / (5 - 3)

= 2(√5 + √3) / 2

= √5 + √3

2). (√3 - 1)/(√3 + 1)

(√3-1)/(√3+1) = (√3-1)(√3-1) / (√3+1)(√3-1)

= (√3 - 1)² / (√3² - 1²)

= (√3² - 2•√3•1 + 1²) / (3 - 1)

= (3 - 2√3 + 1) / 2

= (4 - 2√3) / 2

= 2(2 - √3) / 2

= 2 - √3