Question

Rationalise the denominator of 1/(2√5 + √3)​

Answer 1

`\bf ➤ \underline{Solution-} \\`

`\sf \: \: \: (1)/( 2 √(5) + √(3) )`

On rationalising,

`\sf \implies(1)/( 2 √(5) + √(3) ) * (2 √(5) - √(3))/(2 √(5) - √(3))`

Combine the fractions,

`\sf \implies (1(2 √(5) - √(3)))/((2 √(5) + √(3))(2 √(5) - √(3)))`

We know that,

`\sf \implies (a + b)(a - b) = (a)^(2) - (b)^(2)`

So,

`\sf \implies (1(2 √(5) - √(3)))/((2 √(5) )^(2) - (√(3))^(2) )`

`\sf \implies (1(2 √(5) - √(3)))/(20 - 3 )`

`\sf \implies (1(2 √(5) - √(3)))/(17 )`

`\sf \implies (2 √(5) - √(3))/(17 )`

Hence,

On rationalising we got,

`\bf \implies(2 √(5) - √(3))/(17 )`