Question

square root 2 + square root 3 / 3 square root 2 minus 2 square root 3 is in the form as is equal to a + b square root b​

Answer 1

Step-by-step explanation:

√2+√3/3√2-2√3=a+b√b

L.H.S=√2+√3/3√2-2√3

R.S.H=a+b√b

L.H.S,

=√2+√3/3√2-2√3

=(√2+√3)×(3√2+2√3)/(3√2-2√3). (3√2+2√3) ..... [Rationalising the denominator]

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

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

=(3×2+2√6)+(3√6+2×3)/

(9×2+6√6)-(6√6+4×3)

=(6+2√6)+(3√6+6)/(18+6√6)-(6√6+12)

=6+2√6+3√6+6/18+6√6-6√6+12

=6+6+2√6+3√6/18+12

=12+5√6/18+12

=5√6/18

5√6/18=a+b√b