Question

1/3√2-2√3 simplify each of the following by rationalizing the denominator​

Answer 1

Answer:

Step-by-step explanation:

Rationalising means mulplying the numerator and denominator by the denominator if the denominator is a surd in one variable eg; √a where a ≥ 0  and if it is a surd in two variables eg; √a + √b multiply the numerator and denominator by the denominator changing the arithmetic sign (that is by √a - √b)

⇒ 1/(3√2 - 2√3)= [1 × (3√2 + 2√3) ]/[(3√2 - 2√3) × (3√2 + 2√3) ]

                          = (3√2 + 2√3)/(3√2 - 2√3)(3√2 + 2√3)

                          = (3√2 + 2√3)/(9√4 + 6√6 - 6√6 - 4√9)

                          = (3√2 + 2√3)/(9×2 + 0 - 4×3)

                          = (3√2 + 2√3)/(18 - 12)

                          = (3√2 + 2√3)/6

                          = [(3√2)/6 ] + [(2√3)/6]

                          = (√2/2) + (√3/3)