(5√9-5√3)(5√8+5√27) please multiply

I was not able to find a symbol for the 5th root so I am using 5√. Thank for any help!

(⁵√9 − ⁵√3) (⁵√8 + ⁵√27)
= ⁵√72 + ⁵√243 − ⁵√24 − ⁵√81
= 3 + ⁵√72 − ⁵√24 − ⁵√81

Sometimes people use the caret symbol "^" for roots as well as for powers........

You can do this two ways.........

(1). (5^√9 - 5^√3)(5^√8 + 5^√27) = 5^√72 - 5^√24 + 5^√243 - 5^√81
= 5^√72 - 5^√24 - 5^√81 + 36 = 2.3521 - 1.8881 - 2.4082 + 3 = 1.0558

(2). (1.5518 - 1.2457)(1.5157 + 1.9331 = 0.3061 x 3.4488 = 1.0557

The difference is rounding error

(5√9-5√3)(5√8+5√27)
= (5*3-5√3)(10√2+15√3)
= (15 -5√3)(10√2+15√3)
=150√2+225√3-50√6-225
=25( 6√2+9√3-2√6-9)

(5√9-5√3)(5√8+5√27)
= (9^1/5 -3^1/5)(8^1/5+ 27^1/5)
= (3^2/5 -3^1/5)( 2^3/5 + 3^3/5)
=(3^2*2^3)^1/5+3-(3*2^3)^1/5 - 3^4/5

=1622.498074

=1622.498074