Square Root of 136 Simplified

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What is the square root of 136 simplified?

Answer

√136 = 2√34

136 = 4 × 34, and 4 = 2² is the largest perfect square that divides 136, so √136 = √4 × √34 = 2√34. Check: 2√34 ≈ 11.662, the same as √136 ≈ 11.662.

Simplifying √136 Step by Step

1. Prime factorization. — All Prime Factors of 136:

136 = 2 × 2 × 2 × 17 = 23 × 17

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 136Comes out of the rootStays under the root
2322
171—17

3. Take the pairs out of the root.

√136 = √((2 × 2) × 2 × 17)

= 2 × √(2 × 17)

= 2√34

4. Check by squaring back.

2² × 34 = 4 × 34 = 136

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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
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

FAQ

What is the square root of 136 simplified?

√136 = 2√34

Is 136 a perfect square?

No. 136 = 4 × 34: its largest perfect square factor is 4 = 2², and the factor 34 stays under the radical, so √136 = 2√34.

What is √136 as a decimal?

√136 ≈ 11.662. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√34.

What is the largest perfect square that divides 136?

4 = 2². Dividing gives 136 ÷ 4 = 34, and 34 has no square factor left, so √136 = √4 × √34 = 2√34.

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