Discussion

Explanation:

Cube-root of 26 + 15√3 will be of the form x + √y

Now, 26 + 15√3 = (x + √y)³

⇒ 26 + 15√3 = x³ + y√y + 3x²√y + 3xy

⇒ 26 + 15√3 = (x³ + 3xy) +  (y + 3x²)√y

By comparing rational and irrational terms on both sides

√y = √3 ⇒ y = 3

and, x³ + 3xy = 26
⇒ x³ + 9x = 26
⇒ x = 2 (by trial and error)

∴ Cube-root of 26 + 15√3 = 2 + √3

Hence, option (c).

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