Nth Root Calculator
A radical expression contains a root symbol (√). The nth root of x: ⁿ√x = x^(1/n). Square roots (n=2) are most common. Simplifying radicals means removing perfect square factors from inside the radical.
💡
Tip: To simplify a radical: find the largest perfect square factor. √200 = √(100×2) = 10√2 is simpler than √(4×50) = 2√50 — always use the LARGEST perfect square factor.
- 1√(ab) = √a × √b (product rule for radicals)
- 2√(a/b) = √a / √b (quotient rule)
- 3Simplify: √72 = √(36×2) = 6√2
- 4Rationalize denominator: 1/√2 = √2/2
√48=4√3√(16×3) = 4√3
∛(54)=3∛2∛(27×2) = 3∛2
√(x²y⁴)=xy²Assuming x,y ≥ 0
| n | n² | n³ |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1,000 |
⭐
Fun Fact
The ancient Greeks were disturbed by irrational numbers like √2 = 1.41421356... (non-repeating, non-terminating). The Pythagorean school allegedly drowned Hippasus for proving √2 couldn't be expressed as a fraction — though this story is probably legend.
References
🔒
୧୦୦% ମାଗଣା
ପଞ୍ଜୀକରଣ ଆବଶ୍ୟକ ନାହିଁ
✓
ସଠିକ
ଯାଞ୍ଚ ହୋଇଥିବା ସୂତ୍ର
⚡
ତତ୍କ୍ଷଣ
ତତ୍କ୍ଷଣ ଫଳ
📱
ମୋବାଇଲ୍ ଅନୁକୂଳ
ସମସ୍ତ ଡିଭାଇସ୍