Square Root of 138 Simplified

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What is the square root of 138 simplified?

Answer

√138 cannot be simplified — its simplest radical form is
√138

√138 is already in simplest form — 138 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √138 ≈ 11.747.

Simplifying √138 Step by Step

1. Prime factorization. — All Prime Factors of 138:

138 = 2 × 3 × 23

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 138Comes out of the rootStays under the root
21—2
31—3
231—23

3. Take the pairs out of the root.

√138 = √(2 × 3 × 23)

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

√138

4. Check by squaring back.

The only perfect square dividing 138 is 1 = 1², and 1² × 138 = 138

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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 138 simplified? (The answer is: √138). Enter a whole number (e.g. '138') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
123√123≈ 11.091
1242√31≈ 11.136
1255√5≈ 11.18
1263√14≈ 11.225
127√127≈ 11.269
1288√2≈ 11.314
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

FAQ

What is the square root of 138 simplified?

√138 cannot be simplified — its simplest radical form is √138

Is 138 a perfect square?

No. 138 has no perfect square factor other than 1, so √138 cannot be simplified and stays √138.

What is √138 as a decimal?

√138 ≈ 11.747. The decimal never ends and never repeats, so it is always rounded; the exact value is √138.

What is the largest perfect square that divides 138?

Only 1. 138 has no other square factor, so √138 is already in simplest radical form.

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