Question

Rationalisie the denominator of: 4√3/2-√2​

Answer 1

`\longmapsto4 √(3) + 2 √(6) .`

Explanation:

`\sf{(4√(3))/(2 - √(2))}`

By Rationalizing the denominator:-

`= \sf{(4√(3))/(2 - √(2)) * (2 + √(2))/(2 + √(2))}`

`= \sf{(4√(3)(2 + √(2)))/((2)^2 - (√(2))^2)}`

`= \sf{(4√(3)(2 + √(2)))/(4 - 2)}`

`= \sf{(4√(3)(2 + √(2)))/(2)}`

`= \sf{\frac{\\ot{4}√(3)(2 + √(2))}{\\ot{2}}}`

`= \sf{2√(3)(2 + √(2))}`

`= \sf{4√(3) + 2√(6)}`

`\therefore \sf{(4√(3))/(2 - √(2)) = 4√(3) + 2√(6)}`