Square Root of 3 Simplified

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What is the square root of 3 simplified?

Answer

√3 cannot be simplified — its simplest radical form is
√3

√3 is already in simplest form — 3 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √3 ≈ 1.732.

Simplifying √3 Step by Step

1. Prime factorization. — All Prime Factors of 3:

3 is a prime number

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

3. Take the pairs out of the root.

No prime appears twice, so there is no pair to take out.

√3

4. Check by squaring back.

The only perfect square dividing 3 is 1 = 1², and 1² × 3 = 3

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Simplify Square Root Calculator

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 3 simplified? (The answer is: √3). Enter a whole number (e.g. '3') 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 3 simplified?

√3 cannot be simplified — its simplest radical form is √3

Is 3 a perfect square?

No. 3 has no perfect square factor other than 1, so √3 cannot be simplified and stays √3.

What is √3 as a decimal?

√3 ≈ 1.732. The decimal never ends and never repeats, so it is always rounded; the exact value is √3.

What is the largest perfect square that divides 3?

Only 1. 3 has no other square factor, so √3 is already in simplest radical form.

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