Square Root of 104 Simplified

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What is the square root of 104 simplified?

Answer

√104 = 2√26

104 = 4 × 26, and 4 = 2² is the largest perfect square that divides 104, so √104 = √4 × √26 = 2√26. Check: 2√26 ≈ 10.198, the same as √104 ≈ 10.198.

Simplifying √104 Step by Step

1. Prime factorization. — All Prime Factors of 104:

104 = 2 × 2 × 2 × 13 = 23 × 13

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 104Comes out of the rootStays under the root
2322
131—13

3. Take the pairs out of the root.

√104 = √((2 × 2) × 2 × 13)

= 2 × √(2 × 13)

= 2√26

4. Check by squaring back.

2² × 26 = 4 × 26 = 104

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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 104 simplified? (The answer is: 2√26). Enter a whole number (e.g. '104') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
89√89≈ 9.434
903√10≈ 9.487
91√91≈ 9.539
922√23≈ 9.592
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

FAQ

What is the square root of 104 simplified?

√104 = 2√26

Is 104 a perfect square?

No. 104 = 4 × 26: its largest perfect square factor is 4 = 2², and the factor 26 stays under the radical, so √104 = 2√26.

What is √104 as a decimal?

√104 ≈ 10.198. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√26.

What is the largest perfect square that divides 104?

4 = 2². Dividing gives 104 ÷ 4 = 26, and 26 has no square factor left, so √104 = √4 × √26 = 2√26.

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