Square Root of 146 Simplified

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What is the square root of 146 simplified?

Answer

√146 cannot be simplified — its simplest radical form is
√146

√146 is already in simplest form — 146 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √146 ≈ 12.083.

Simplifying √146 Step by Step

1. Prime factorization. — All Prime Factors of 146:

146 = 2 × 73

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 146Comes out of the rootStays under the root
21—2
731—73

3. Take the pairs out of the root.

√146 = √(2 × 73)

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

√146

4. Check by squaring back.

The only perfect square dividing 146 is 1 = 1², and 1² × 146 = 146

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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 146 simplified? (The answer is: √146). Enter a whole number (e.g. '146') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
131√131≈ 11.446
1322√33≈ 11.489
133√133≈ 11.533
134√134≈ 11.576
1353√15≈ 11.619
1362√34≈ 11.662
137√137≈ 11.705
138√138≈ 11.747
139√139≈ 11.79
1402√35≈ 11.832
141√141≈ 11.874
142√142≈ 11.916
143√143≈ 11.958
1441212
145√145≈ 12.042
146√146≈ 12.083
1477√3≈ 12.124
1482√37≈ 12.166
149√149≈ 12.207
1505√6≈ 12.247
151√151≈ 12.288
1522√38≈ 12.329
1533√17≈ 12.369
154√154≈ 12.41
155√155≈ 12.45
1562√39≈ 12.49
157√157≈ 12.53
158√158≈ 12.57
159√159≈ 12.61
1604√10≈ 12.649

FAQ

What is the square root of 146 simplified?

√146 cannot be simplified — its simplest radical form is √146

Is 146 a perfect square?

No. 146 has no perfect square factor other than 1, so √146 cannot be simplified and stays √146.

What is √146 as a decimal?

√146 ≈ 12.083. The decimal never ends and never repeats, so it is always rounded; the exact value is √146.

What is the largest perfect square that divides 146?

Only 1. 146 has no other square factor, so √146 is already in simplest radical form.

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