Question

Simplify
3 root 2 - 2 root 3/root8+root27

Answer 1

Answer:

-57√2-4√6+18/-19

Step-by-step explanation:

given : 3√2 - 2√3/√8+√27

we can write √8 and √27 as 2√2 and 3√3 respectively

then 3√2 - 2√3/ 2√2+3√3

Now taking the LCM

3√2 (2√2+3√3) - 2√3 / 2√2+3√3

= 12+9√6 -2√3 / 2√2+3√3. (1)

Now on rationalising the eq (1)

12+9√6-2√3 × 2√2-3√3 / (2√2+3√3)(2√2-3√3)

on using the identity{ (a+b)(a-b)=a^2-b^2 } we get

24√2+36√3-4√6-36√3-81√2+18 / 2√2^2-3√3^2

= -57√2-4√6+18/-19