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15 Mar 2026, 12:21
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Hi everyone,
I recently struggled with rational roots/exponents such as the “1.5-th root” and wanted to share a simple mental framework that helped me.
Key idea:
A b-th root is the same as raising to the power 1/b.
So:
1.5 = 3/2
→ 1 / 1.5 = 2/3
That means:
1.5-th root of x = x^(2/3) = cube root of (x^2)
Example:
(1.5-root of 2)^3 = (2^(2/3))^3 = 2^2 = 4
Mental shortcut:
• 1.5-root = square first, then cube root
• Much easier than thinking in decimals
This helped me a lot on DS questions where exact values are not required, only comparisons.
Would love to hear if others use a different intuition or shortcut.
I recently struggled with rational roots/exponents such as the “1.5-th root” and wanted to share a simple mental framework that helped me.
Key idea:
A b-th root is the same as raising to the power 1/b.
So:
1.5 = 3/2
→ 1 / 1.5 = 2/3
That means:
1.5-th root of x = x^(2/3) = cube root of (x^2)
Example:
(1.5-root of 2)^3 = (2^(2/3))^3 = 2^2 = 4
Mental shortcut:
• 1.5-root = square first, then cube root
• Much easier than thinking in decimals
This helped me a lot on DS questions where exact values are not required, only comparisons.
Would love to hear if others use a different intuition or shortcut.
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