Question

simplify :-
$(5( {8}^{1\3} + {27}^{1 \3}) ^{3})^{1 \4}$
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Answer 1

first we can write 8^1/3 and 27^1/3 as 3√ 8 and 3√ 27 respectively

so it will be,

{5[3√8 + 3√27] ^3}^1/4

{5[2+3]^3}^1/4

NOW WE WILL USE THE IDENTITY [A+B]^3=A^3+B^3+3AB[A+B]

so it will be ,

{5[8+27+90]}^1/4

{5[125]}^1/4

(625)^1/4

now we can write it as 4√625

so the answer will come as

=5