Square Root of 212 Simplified

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What is the square root of 212 simplified?

Answer

√212 = 2√53

212 = 4 × 53, and 4 = 2² is the largest perfect square that divides 212, so √212 = √4 × √53 = 2√53. Check: 2√53 ≈ 14.56, the same as √212 ≈ 14.56.

Simplifying √212 Step by Step

1. Prime factorization. — All Prime Factors of 212:

212 = 2 × 2 × 53 = 22 × 53

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 212Comes out of the rootStays under the root
222—
531—53

3. Take the pairs out of the root.

√212 = √((2 × 2) × 53)

= 2 × √53

= 2√53

4. Check by squaring back.

2² × 53 = 4 × 53 = 212

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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 212 simplified? (The answer is: 2√53). Enter a whole number (e.g. '212') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
197√197≈ 14.036
1983√22≈ 14.071
199√199≈ 14.107
20010√2≈ 14.142
201√201≈ 14.177
202√202≈ 14.213
203√203≈ 14.248
2042√51≈ 14.283
205√205≈ 14.318
206√206≈ 14.353
2073√23≈ 14.387
2084√13≈ 14.422
209√209≈ 14.457
210√210≈ 14.491
211√211≈ 14.526
2122√53≈ 14.56
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

FAQ

What is the square root of 212 simplified?

√212 = 2√53

Is 212 a perfect square?

No. 212 = 4 × 53: its largest perfect square factor is 4 = 2², and the factor 53 stays under the radical, so √212 = 2√53.

What is √212 as a decimal?

√212 ≈ 14.56. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√53.

What is the largest perfect square that divides 212?

4 = 2². Dividing gives 212 ÷ 4 = 53, and 53 has no square factor left, so √212 = √4 × √53 = 2√53.

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