Value of (√2)³:

Question

Value of (√2)³:

1. A. 8
2. B. 2
3. C. 2√2 (Correct answer)
4. D. None of the above

Correct Answer

Option C — 2√2

Detailed Solution & Explanation

The correct answer is 2√2.

Key Points

• (√2)³ = √2 × √2 × √2.
• The first two give √2 × √2 = 2, leaving 2 × √2 = 2√2.
• Numerically that is about 2.83, so the answer is neither 8 nor 2.

Additional Information

• Using index laws: (√2)³ = (2^½)³ = 2^(3/2) = 2¹ × 2^½ = 2√2.
• The rule to carry: (√a)ⁿ = a^(n/2), and √a × √a = a.
• Values worth memorising: √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236.