Square Root of 100 Simplified

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What is the square root of 100 simplified?

Answer

√100 = 10

100 is a perfect square — 100 = 10², so no radical remains: √100 = 10.

Simplifying √100 Step by Step

1. Prime factorization. — All Prime Factors of 100:

100 = 2 × 2 × 5 × 5 = 22 × 52

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 100Comes out of the rootStays under the root
222—
525—

3. Take the pairs out of the root.

√100 = √((2 × 2) × (5 × 5))

= 2 × 5

= 10

4. Check by squaring back.

10² = 10 × 10 = 100

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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 100 simplified? (The answer is: 10). Enter a whole number (e.g. '100') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
85√85≈ 9.22
86√86≈ 9.274
87√87≈ 9.327
882√22≈ 9.381
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

FAQ

What is the square root of 100 simplified?

√100 = 10

Is 100 a perfect square?

Yes: 100 = 10², so √100 = 10 exactly and nothing stays under the radical.

What is √100 as a decimal?

√100 = 10 exactly — a whole number, because 100 is a perfect square.

What is the largest perfect square that divides 100?

100 itself: it is 10², so √100 = 10.

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