Square Root of 253 Simplified

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What is the square root of 253 simplified?

Answer

√253 cannot be simplified — its simplest radical form is
√253

√253 is already in simplest form — 253 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √253 ≈ 15.906.

Simplifying √253 Step by Step

1. Prime factorization. — All Prime Factors of 253:

253 = 11 × 23

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 253Comes out of the rootStays under the root
111—11
231—23

3. Take the pairs out of the root.

√253 = √(11 × 23)

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

√253

4. Check by squaring back.

The only perfect square dividing 253 is 1 = 1², and 1² × 253 = 253

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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 253 simplified? (The answer is: √253). Enter a whole number (e.g. '253') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
238√238≈ 15.427
239√239≈ 15.46
2404√15≈ 15.492
241√241≈ 15.524
24211√2≈ 15.556
2439√3≈ 15.588
2442√61≈ 15.62
2457√5≈ 15.652
246√246≈ 15.684
247√247≈ 15.716
2482√62≈ 15.748
249√249≈ 15.78
2505√10≈ 15.811
251√251≈ 15.843
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

FAQ

What is the square root of 253 simplified?

√253 cannot be simplified — its simplest radical form is √253

Is 253 a perfect square?

No. 253 has no perfect square factor other than 1, so √253 cannot be simplified and stays √253.

What is √253 as a decimal?

√253 ≈ 15.906. The decimal never ends and never repeats, so it is always rounded; the exact value is √253.

What is the largest perfect square that divides 253?

Only 1. 253 has no other square factor, so √253 is already in simplest radical form.

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