Square Root of 267 Simplified

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What is the square root of 267 simplified?

Answer

√267 cannot be simplified — its simplest radical form is
√267

√267 is already in simplest form — 267 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √267 ≈ 16.34.

Simplifying √267 Step by Step

1. Prime factorization. — All Prime Factors of 267:

267 = 3 × 89

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 267Comes out of the rootStays under the root
31—3
891—89

3. Take the pairs out of the root.

√267 = √(3 × 89)

No prime appears twice, so there is no pair to take out.

√267

4. Check by squaring back.

The only perfect square dividing 267 is 1 = 1², and 1² × 267 = 267

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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 267 simplified? (The answer is: √267). Enter a whole number (e.g. '267') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
2526√7≈ 15.875
253√253≈ 15.906
254√254≈ 15.937
255√255≈ 15.969
2561616
257√257≈ 16.031
258√258≈ 16.062
259√259≈ 16.093
2602√65≈ 16.125
2613√29≈ 16.155
262√262≈ 16.186
263√263≈ 16.217
2642√66≈ 16.248
265√265≈ 16.279
266√266≈ 16.31
267√267≈ 16.34
2682√67≈ 16.371
269√269≈ 16.401
2703√30≈ 16.432
271√271≈ 16.462
2724√17≈ 16.492
273√273≈ 16.523
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

FAQ

What is the square root of 267 simplified?

√267 cannot be simplified — its simplest radical form is √267

Is 267 a perfect square?

No. 267 has no perfect square factor other than 1, so √267 cannot be simplified and stays √267.

What is √267 as a decimal?

√267 ≈ 16.34. The decimal never ends and never repeats, so it is always rounded; the exact value is √267.

What is the largest perfect square that divides 267?

Only 1. 267 has no other square factor, so √267 is already in simplest radical form.

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