Question

rationalisa the denominator of the following (3+root5 )/ (5_root 3)
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Answer 1

Answer:

Step-by-step explanation:

3 + √5 / 5 - √3

→ 3 + √5 /5 - √3 × 5 + √3/5 + √3

→ 15 + 3√3 + 5√5 + √15 / 5² - (√3)²..........{(a + b)(a - b) = a² - b²}

→ (15 + 3√3 + 5√5 + √15) / 25 - 3

→ (15 + 3√3 + 5√5 + √15) / 22

→ (3 × 5 + 3√3 + 5√5 + √3 × √5)/ 22

Now taking common:

We get,

⇒[ 3(5 + √3) + √5(5 + √3)]/22

Now again taking common,

We get,

↔ [(3 + √5)(5 + √3)]/22

$\frac{[(3 + \sqrt{5} )(5 + \sqrt{3} )]}{22}$