Square Root of 137 Simplified

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What is the square root of 137 simplified?

Answer

√137 cannot be simplified — its simplest radical form is
√137

√137 is already in simplest form — 137 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √137 ≈ 11.705.

Simplifying √137 Step by Step

1. Prime factorization. — All Prime Factors of 137:

137 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 137Comes out of the rootStays under the root
1371—137

3. Take the pairs out of the root.

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

√137

4. Check by squaring back.

The only perfect square dividing 137 is 1 = 1², and 1² × 137 = 137

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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 137 simplified? (The answer is: √137). Enter a whole number (e.g. '137') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
122√122≈ 11.045
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

FAQ

What is the square root of 137 simplified?

√137 cannot be simplified — its simplest radical form is √137

Is 137 a perfect square?

No. 137 has no perfect square factor other than 1, so √137 cannot be simplified and stays √137.

What is √137 as a decimal?

√137 ≈ 11.705. The decimal never ends and never repeats, so it is always rounded; the exact value is √137.

What is the largest perfect square that divides 137?

Only 1. 137 has no other square factor, so √137 is already in simplest radical form.

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