Square Root of 144 Simplified

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What is the square root of 144 simplified?

Answer

√144 = 12

144 is a perfect square — 144 = 12², so no radical remains: √144 = 12.

Simplifying √144 Step by Step

1. Prime factorization. — All Prime Factors of 144:

144 = 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32

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 144Comes out of the rootStays under the root
2422—
323—

3. Take the pairs out of the root.

√144 = √((2 × 2) × (2 × 2) × (3 × 3))

= 2 × 2 × 3

= 12

4. Check by squaring back.

12² = 12 × 12 = 144

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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 144 simplified? (The answer is: 12). Enter a whole number (e.g. '144') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
129√129≈ 11.358
130√130≈ 11.402
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

FAQ

What is the square root of 144 simplified?

√144 = 12

Is 144 a perfect square?

Yes: 144 = 12², so √144 = 12 exactly and nothing stays under the radical.

What is √144 as a decimal?

√144 = 12 exactly — a whole number, because 144 is a perfect square.

What is the largest perfect square that divides 144?

144 itself: it is 12², so √144 = 12.

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