Question

If root2=1.4 and root3=1.7 find value of 4/3 root3-2 root 2+3/3 root3+2 root 2

Answer 1

Doing my best to parse the wordy and ambiguous notation, I get

((4/3)√3 - 2√2+3)/(3√3 + 2√2)
No, that is too weird. How about

4/(3√3-2√2) + 3/(3√3+2√2)

Now we can make a common denominator of
(3√3-2√2)(3√3+2√2) = (3√3)^2 - (2√2)^2 = 27-8 = 21

and we have

4(3√3+2√2) + 3(3√3-2√2)
-----------------------------
21

12√3+8√2+9√3-6√2
-----------------
21

(21√3+2√2)/21
= √3 + (2/21)√2

Though why you would want to go through any of that is unclear, since you apparently want to use the approximate values of √2 and √3. Just use your calculator to evaluate the original expression.

Using your original syntax, that would be

4/3(1.7)-2(1.4)+3/3(1.7)+2(1.4)

I guess you can work out how the terms and factors are grouped together.