Square Root of 108 Simplified

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What is the square root of 108 simplified?

Answer

√108 = 6√3

108 = 36 × 3, and 36 = 6² is the largest perfect square that divides 108, so √108 = √36 × √3 = 6√3. Check: 6√3 ≈ 10.392, the same as √108 ≈ 10.392.

Simplifying √108 Step by Step

1. Prime factorization. — All Prime Factors of 108:

108 = 2 × 2 × 3 × 3 × 3 = 22 × 33

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 108Comes out of the rootStays under the root
222—
3333

3. Take the pairs out of the root.

√108 = √((2 × 2) × (3 × 3) × 3)

= 2 × 3 × √3

= 6√3

4. Check by squaring back.

6² × 3 = 36 × 3 = 108

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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 108 simplified? (The answer is: 6√3). Enter a whole number (e.g. '108') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
93√93≈ 9.644
94√94≈ 9.695
95√95≈ 9.747
964√6≈ 9.798
97√97≈ 9.849
987√2≈ 9.899
993√11≈ 9.95
1001010
101√101≈ 10.05
102√102≈ 10.1
103√103≈ 10.149
1042√26≈ 10.198
105√105≈ 10.247
106√106≈ 10.296
107√107≈ 10.344
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

FAQ

What is the square root of 108 simplified?

√108 = 6√3

Is 108 a perfect square?

No. 108 = 36 × 3: its largest perfect square factor is 36 = 6², and the factor 3 stays under the radical, so √108 = 6√3.

What is √108 as a decimal?

√108 ≈ 10.392. The decimal never ends and never repeats, so it is always rounded; the exact value is 6√3.

What is the largest perfect square that divides 108?

36 = 6². Dividing gives 108 ÷ 36 = 3, and 3 has no square factor left, so √108 = √36 × √3 = 6√3.

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