√320 is irrational — 17.8885 to four decimal places, 17.89 to two
√320 ≈ 17.8885. The trick with a root like this is to spot the biggest square hiding inside the number.
√320 ≈ 17.8885. Rounded to two decimal places that is 17.89.
320 is not a perfect square, so its root is not a whole number. The nearest whole numbers either side are 17 and 18: 17 × 17 = 289 and 18 × 18 = 324, and 320 sits between those two, so √320 sits between 17 and 18.
The root is irrational, which means the decimal never terminates and never settles into a repeating block. 17.8885 is a rounded value, not the exact one — the exact answer can only be written as √320 itself, or in simplified form as 8√5.
Square your answer and see how close it lands. 17.89 × 17.89 = 320.0521, which is within a whisker of 320 — close enough to confirm the root without a calculator agreeing digit for digit.
√320 simplifies to 8√5, because 320 = 64 × 5 and 64 is a perfect square. Pulling the 8 out from under the root sign is the standard way to write it in exact form.
Check it numerically: 8 × √5 = 8 × 2.2361 = 17.8885, the same value as √320. Simplified form is the same number written more tidily, not a different one.
320 = 64 × 5, and 64 is a perfect square. So √320 = √64 × √5 = 8√5. Spotting the biggest square factor is the whole trick to simplifying a root.
√5 ≈ 2.2361, so 8√5 ≈ 17.8885. That is between 17² = 289 and 18² = 324, and much closer to 324 — which matches.
√5 is also the root at the heart of the golden ratio, (1 + √5) ÷ 2 ≈ 1.618, so multiples of √5 turn up in geometry problems involving pentagons and golden rectangles.
320 lies between 289 (17²) and 324 (18²), 31 of the way along a gap of 35, so a quick linear estimate is 17.89. Bracketing between the nearest squares is the fastest mental check for any root.
The square root of 320 is approximately 17.8885, or 17.89 to two decimal places. It is an irrational number, so the decimal does not end.
No. 320 falls between 289 (17²) and 324 (18²), so its square root is not a whole number.
Bracket it between the two nearest square numbers — 289 and 324 — then judge how far along the gap 320 sits. That gets you to roughly 17.89, which is close enough for almost any mental check.
No. 17² = 289 and 18² = 324, so √320 ≈ 17.889 is not a whole number. In simplest radical form it is 8√5.
320² = 102,400. It is 32² = 1,024 with two zeros on the end, because 320 = 32 × 10.
√320 = 8√5, because 320 = 64 × 5 and 64 is a perfect square.
Every square number up to 25² — and the roots people most often look up — is listed on the square numbers page.