Question

If root 2 = 1.414, and root 3 = 1.723, find 4/3 root 3 - 2 root 2 + 3/ 3 root 3 + 2 root 2

Answer 1

4/(3√3 -2√2) + 3/(3√3 + 2√2)

={4(3√3 + 2√2) +3(3√3-2√2)}/(3√3-2√2)(3√3+2√2)

use (a - b)(a + b) = a² -b² in denominator

now,

={12√3+8√2+9√3-6√2}/(27 -8)

=(21√3 +2√2)/(19)

now , put √3 = 1.732 and √2 = 1.414

=(21×1.732 + 2×1.414)/19

=(36.372+ 2.828)/19

=39.2/19

=2.06