Square Root of 2016 Simplified

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What is the square root of 2,016 simplified?

Answer

√2,016 = 12√14

2,016 = 144 × 14, and 144 = 12² is the largest perfect square that divides 2,016, so √2,016 = √144 × √14 = 12√14. Check: 12√14 ≈ 44.9, the same as √2,016 ≈ 44.9.

Simplifying √2,016 Step by Step

1. Prime factorization. — All Prime Factors of 2,016:

2,016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 = 25 × 32 × 7

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 2,016Comes out of the rootStays under the root
25222
323—
71—7

3. Take the pairs out of the root.

√2,016 = √((2 × 2) × (2 × 2) × (3 × 3) × 2 × 7)

= 2 × 2 × 3 × √(2 × 7)

= 12√14

4. Check by squaring back.

12² × 14 = 144 × 14 = 2,016

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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 2,016 simplified? (The answer is: 12√14). Enter a whole number (e.g. '2,016') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
7255√29≈ 26.926
72611√6≈ 26.944
7292727
7505√30≈ 27.386
7566√21≈ 27.495
7722√193≈ 27.785
7802√195≈ 27.928
80020√2≈ 28.284
8505√34≈ 29.155
8755√35≈ 29.58
8804√55≈ 29.665
9608√15≈ 30.984
97218√3≈ 31.177
1,00010√10≈ 31.623
1,20020√3≈ 34.641
1,25025√2≈ 35.355
1,2606√35≈ 35.496
1,28016√5≈ 35.777
1,2963636
1,57515√7≈ 39.686
1,87525√3≈ 43.301
2,00020√5≈ 44.721
2,01612√14≈ 44.9
3,7806√105≈ 61.482
5,00050√2≈ 70.711
7,20060√2≈ 84.853
8,00040√5≈ 89.443
12,50050√5≈ 111.803
20,000100√2≈ 141.421
84,500130√5≈ 290.689

FAQ

What is the square root of 2,016 simplified?

√2,016 = 12√14

Is 2,016 a perfect square?

No. 2,016 = 144 × 14: its largest perfect square factor is 144 = 12², and the factor 14 stays under the radical, so √2,016 = 12√14.

What is √2,016 as a decimal?

√2,016 ≈ 44.9. The decimal never ends and never repeats, so it is always rounded; the exact value is 12√14.

What is the largest perfect square that divides 2,016?

144 = 12². Dividing gives 2,016 ÷ 144 = 14, and 14 has no square factor left, so √2,016 = √144 × √14 = 12√14.

See Also