Square Root of 123 Simplified

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What is the square root of 123 simplified?

Answer

√123 cannot be simplified — its simplest radical form is
√123

√123 is already in simplest form — 123 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √123 ≈ 11.091.

Simplifying √123 Step by Step

1. Prime factorization. — All Prime Factors of 123:

123 = 3 × 41

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 123Comes out of the rootStays under the root
31—3
411—41

3. Take the pairs out of the root.

√123 = √(3 × 41)

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

√123

4. Check by squaring back.

The only perfect square dividing 123 is 1 = 1², and 1² × 123 = 123

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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 123 simplified? (The answer is: √123). Enter a whole number (e.g. '123') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
1086√3≈ 10.392
109√109≈ 10.44
110√110≈ 10.488
111√111≈ 10.536
1124√7≈ 10.583
113√113≈ 10.63
114√114≈ 10.677
115√115≈ 10.724
1162√29≈ 10.77
1173√13≈ 10.817
118√118≈ 10.863
119√119≈ 10.909
1202√30≈ 10.954
1211111
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

FAQ

What is the square root of 123 simplified?

√123 cannot be simplified — its simplest radical form is √123

Is 123 a perfect square?

No. 123 has no perfect square factor other than 1, so √123 cannot be simplified and stays √123.

What is √123 as a decimal?

√123 ≈ 11.091. The decimal never ends and never repeats, so it is always rounded; the exact value is √123.

What is the largest perfect square that divides 123?

Only 1. 123 has no other square factor, so √123 is already in simplest radical form.

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