Question

How is 4 root 54 equal to 12 root 6 and 5 root 96 equal to 20 root 6 ?

Answer 1

4√54 = 12√6

Splitting 54 as (9×6),

4√(9×6) = 12√6

4×√9×√6 = 12√6

4×3 ×√6 = 12√6 [√9=3]

12× √6 = 12√6

12√6 = 12√ 6.

Hence proved.

5√96 = 20√6

Splitting 96 as(16×6),

5√(16×6) = 20√6

5×√16×√6 = 20√6

5×4 × √6 = 20√6

20 × √6 = 20√6

20√6 = 20√6

Hence proved.

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