Square Root of 228 Simplified

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What is the square root of 228 simplified?

Answer

√228 = 2√57

228 = 4 × 57, and 4 = 2² is the largest perfect square that divides 228, so √228 = √4 × √57 = 2√57. Check: 2√57 ≈ 15.1, the same as √228 ≈ 15.1.

Simplifying √228 Step by Step

1. Prime factorization. — All Prime Factors of 228:

228 = 2 × 2 × 3 × 19 = 22 × 3 × 19

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 228Comes out of the rootStays under the root
222—
31—3
191—19

3. Take the pairs out of the root.

√228 = √((2 × 2) × 3 × 19)

= 2 × √(3 × 19)

= 2√57

4. Check by squaring back.

2² × 57 = 4 × 57 = 228

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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 228 simplified? (The answer is: 2√57). Enter a whole number (e.g. '228') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
213√213≈ 14.595
214√214≈ 14.629
215√215≈ 14.663
2166√6≈ 14.697
217√217≈ 14.731
218√218≈ 14.765
219√219≈ 14.799
2202√55≈ 14.832
221√221≈ 14.866
222√222≈ 14.9
223√223≈ 14.933
2244√14≈ 14.967
2251515
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

FAQ

What is the square root of 228 simplified?

√228 = 2√57

Is 228 a perfect square?

No. 228 = 4 × 57: its largest perfect square factor is 4 = 2², and the factor 57 stays under the radical, so √228 = 2√57.

What is √228 as a decimal?

√228 ≈ 15.1. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√57.

What is the largest perfect square that divides 228?

4 = 2². Dividing gives 228 ÷ 4 = 57, and 57 has no square factor left, so √228 = √4 × √57 = 2√57.

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