Square Root of 242 Simplified

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What is the square root of 242 simplified?

Answer

√242 = 11√2

242 = 121 × 2, and 121 = 11² is the largest perfect square that divides 242, so √242 = √121 × √2 = 11√2. Check: 11√2 ≈ 15.556, the same as √242 ≈ 15.556.

Simplifying √242 Step by Step

1. Prime factorization. — All Prime Factors of 242:

242 = 2 × 11 × 11 = 2 × 112

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 242Comes out of the rootStays under the root
21—2
11211—

3. Take the pairs out of the root.

√242 = √((11 × 11) × 2)

= 11 × √2

= 11√2

4. Check by squaring back.

11² × 2 = 121 × 2 = 242

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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 242 simplified? (The answer is: 11√2). Enter a whole number (e.g. '242') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
2561616

FAQ

What is the square root of 242 simplified?

√242 = 11√2

Is 242 a perfect square?

No. 242 = 121 × 2: its largest perfect square factor is 121 = 11², and the factor 2 stays under the radical, so √242 = 11√2.

What is √242 as a decimal?

√242 ≈ 15.556. The decimal never ends and never repeats, so it is always rounded; the exact value is 11√2.

What is the largest perfect square that divides 242?

121 = 11². Dividing gives 242 ÷ 121 = 2, and 2 has no square factor left, so √242 = √121 × √2 = 11√2.

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