Square Root of 12 Simplified

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What is the square root of 12 simplified?

Answer

√12 = 2√3

12 = 4 × 3, and 4 = 2² is the largest perfect square that divides 12, so √12 = √4 × √3 = 2√3. Check: 2√3 ≈ 3.464, the same as √12 ≈ 3.464.

Simplifying √12 Step by Step

1. Prime factorization. — All Prime Factors of 12:

12 = 2 × 2 × 3 = 22 × 3

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 12Comes out of the rootStays under the root
222—
31—3

3. Take the pairs out of the root.

√12 = √((2 × 2) × 3)

= 2 × √3

= 2√3

4. Check by squaring back.

2² × 3 = 4 × 3 = 12

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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 12 simplified? (The answer is: 2√3). Enter a whole number (e.g. '12') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
2√2≈ 1.414
3√3≈ 1.732
422
5√5≈ 2.236
6√6≈ 2.449
7√7≈ 2.646
82√2≈ 2.828
933
10√10≈ 3.162
11√11≈ 3.317
122√3≈ 3.464
13√13≈ 3.606
14√14≈ 3.742
15√15≈ 3.873
1644
17√17≈ 4.123
183√2≈ 4.243
19√19≈ 4.359
202√5≈ 4.472
21√21≈ 4.583
22√22≈ 4.69
23√23≈ 4.796
242√6≈ 4.899
2555
26√26≈ 5.099
273√3≈ 5.196
282√7≈ 5.292
29√29≈ 5.385
30√30≈ 5.477
31√31≈ 5.568

FAQ

What is the square root of 12 simplified?

√12 = 2√3

Is 12 a perfect square?

No. 12 = 4 × 3: its largest perfect square factor is 4 = 2², and the factor 3 stays under the radical, so √12 = 2√3.

What is √12 as a decimal?

√12 ≈ 3.464. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√3.

What is the largest perfect square that divides 12?

4 = 2². Dividing gives 12 ÷ 4 = 3, and 3 has no square factor left, so √12 = √4 × √3 = 2√3.

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