Square Root of 273 Simplified

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What is the square root of 273 simplified?

Answer

√273 cannot be simplified — its simplest radical form is
√273

√273 is already in simplest form — 273 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √273 ≈ 16.523.

Simplifying √273 Step by Step

1. Prime factorization. — All Prime Factors of 273:

273 = 3 × 7 × 13

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 273Comes out of the rootStays under the root
31—3
71—7
131—13

3. Take the pairs out of the root.

√273 = √(3 × 7 × 13)

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

√273

4. Check by squaring back.

The only perfect square dividing 273 is 1 = 1², and 1² × 273 = 273

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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 273 simplified? (The answer is: √273). Enter a whole number (e.g. '273') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
282√282≈ 16.793
283√283≈ 16.823
2842√71≈ 16.852
285√285≈ 16.882
286√286≈ 16.912
287√287≈ 16.941

FAQ

What is the square root of 273 simplified?

√273 cannot be simplified — its simplest radical form is √273

Is 273 a perfect square?

No. 273 has no perfect square factor other than 1, so √273 cannot be simplified and stays √273.

What is √273 as a decimal?

√273 ≈ 16.523. The decimal never ends and never repeats, so it is always rounded; the exact value is √273.

What is the largest perfect square that divides 273?

Only 1. 273 has no other square factor, so √273 is already in simplest radical form.

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