Square Root of 241 Simplified

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What is the square root of 241 simplified?

Answer

√241 cannot be simplified — its simplest radical form is
√241

√241 is already in simplest form — 241 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √241 ≈ 15.524.

Simplifying √241 Step by Step

1. Prime factorization. — All Prime Factors of 241:

241 is a prime number

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 241Comes out of the rootStays under the root
2411—241

3. Take the pairs out of the root.

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

√241

4. Check by squaring back.

The only perfect square dividing 241 is 1 = 1², and 1² × 241 = 241

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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 241 simplified? (The answer is: √241). Enter a whole number (e.g. '241') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
226√226≈ 15.033
227√227≈ 15.067
2282√57≈ 15.1
229√229≈ 15.133
230√230≈ 15.166
231√231≈ 15.199
2322√58≈ 15.232
233√233≈ 15.264
2343√26≈ 15.297
235√235≈ 15.33
2362√59≈ 15.362
237√237≈ 15.395
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

FAQ

What is the square root of 241 simplified?

√241 cannot be simplified — its simplest radical form is √241

Is 241 a perfect square?

No. 241 has no perfect square factor other than 1, so √241 cannot be simplified and stays √241.

What is √241 as a decimal?

√241 ≈ 15.524. The decimal never ends and never repeats, so it is always rounded; the exact value is √241.

What is the largest perfect square that divides 241?

Only 1. 241 has no other square factor, so √241 is already in simplest radical form.

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