Question

Rationalise the denominator and simplify (3√2/√3+√6)-(4√3/√6+√2)+(6/√2+√3)

Answer 1

Answer:

(3√2) /(√3+√6) = [ { (3√2) × (-√3+√6) } / {(√3+√6) × (-√3+√6)} ] = (- 3√6 + 3√12)/(3) = √12 - √6 = 2√3 - √6. (4√3) /(√2+√6) = [ { (4√3) × (-√2+√6) } / {(√2+√6) × (-√2+√6)} ] = (- 4√6 + 4√18)/(4) = √18 - √6 = 3√2 - √6.(√6) /(√3+√2) = [ { (√6) × (-√2+√3) } / {(√3 + √2) × (-√2+√3)} ] = (- √12 + √18)/(1) = -√12 + √18 = 3√2 - 2√3. So, (3√2) /(√3+√6) + (4√3) /(√2+√6) + (√6) /(√3+√2) = 2√3 - √6. + 3√2 - √6. + 3√2 - 2√3. = 6√2 - 2√6

4.3