Square Root of 149 Simplified

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What is the square root of 149 simplified?

Answer

√149 cannot be simplified — its simplest radical form is
√149

√149 is already in simplest form — 149 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √149 ≈ 12.207.

Simplifying √149 Step by Step

1. Prime factorization. — All Prime Factors of 149:

149 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 149Comes out of the rootStays under the root
1491—149

3. Take the pairs out of the root.

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

√149

4. Check by squaring back.

The only perfect square dividing 149 is 1 = 1², and 1² × 149 = 149

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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 149 simplified? (The answer is: √149). Enter a whole number (e.g. '149') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
161√161≈ 12.689
1629√2≈ 12.728
163√163≈ 12.767

FAQ

What is the square root of 149 simplified?

√149 cannot be simplified — its simplest radical form is √149

Is 149 a perfect square?

No. 149 has no perfect square factor other than 1, so √149 cannot be simplified and stays √149.

What is √149 as a decimal?

√149 ≈ 12.207. The decimal never ends and never repeats, so it is always rounded; the exact value is √149.

What is the largest perfect square that divides 149?

Only 1. 149 has no other square factor, so √149 is already in simplest radical form.

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