Square Root of 289 Simplified

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What is the square root of 289 simplified?

Answer

√289 = 17

289 is a perfect square — 289 = 17², so no radical remains: √289 = 17.

Simplifying √289 Step by Step

1. Prime factorization. — All Prime Factors of 289:

289 = 17 × 17 = 172

2. Pair up equal primes. Each pair is a perfect square and comes out of the root as one factor; a prime without a partner stays under the radical.

Prime factorTimes in 289Comes out of the rootStays under the root
17217—

3. Take the pairs out of the root.

√289 = √(17 × 17)

= 17

4. Check by squaring back.

17² = 17 × 17 = 289

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This calculator writes a square root in simplest radical form: it finds the largest perfect square that divides the number, takes its root out of the radical and leaves the rest under it. For example, it can help you find out what is the square root of 289 simplified? (The answer is: 17). Enter a whole number (e.g. '289') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
274√274≈ 16.553
2755√11≈ 16.583
2762√69≈ 16.613
277√277≈ 16.643
278√278≈ 16.673
2793√31≈ 16.703
2802√70≈ 16.733
281√281≈ 16.763
282√282≈ 16.793
283√283≈ 16.823
2842√71≈ 16.852
285√285≈ 16.882
286√286≈ 16.912
287√287≈ 16.941
28812√2≈ 16.971
2891717
290√290≈ 17.029
291√291≈ 17.059
2922√73≈ 17.088
293√293≈ 17.117
2947√6≈ 17.146
295√295≈ 17.176
2962√74≈ 17.205
2973√33≈ 17.234
298√298≈ 17.263
299√299≈ 17.292
30010√3≈ 17.321
3122√78≈ 17.664
3255√13≈ 18.028
330√330≈ 18.166

FAQ

What is the square root of 289 simplified?

√289 = 17

Is 289 a perfect square?

Yes: 289 = 17², so √289 = 17 exactly and nothing stays under the radical.

What is √289 as a decimal?

√289 = 17 exactly — a whole number, because 289 is a perfect square.

What is the largest perfect square that divides 289?

289 itself: it is 17², so √289 = 17.

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