Square Root of 112 Simplified

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What is the square root of 112 simplified?

Answer

√112 = 4√7

112 = 16 × 7, and 16 = 4² is the largest perfect square that divides 112, so √112 = √16 × √7 = 4√7. Check: 4√7 ≈ 10.583, the same as √112 ≈ 10.583.

Simplifying √112 Step by Step

1. Prime factorization. — All Prime Factors of 112:

112 = 2 × 2 × 2 × 2 × 7 = 24 × 7

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 112Comes out of the rootStays under the root
2422—
71—7

3. Take the pairs out of the root.

√112 = √((2 × 2) × (2 × 2) × 7)

= 2 × 2 × √7

= 4√7

4. Check by squaring back.

4² × 7 = 16 × 7 = 112

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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
123√123≈ 11.091
1242√31≈ 11.136
1255√5≈ 11.18
1263√14≈ 11.225

FAQ

What is the square root of 112 simplified?

√112 = 4√7

Is 112 a perfect square?

No. 112 = 16 × 7: its largest perfect square factor is 16 = 4², and the factor 7 stays under the radical, so √112 = 4√7.

What is √112 as a decimal?

√112 ≈ 10.583. The decimal never ends and never repeats, so it is always rounded; the exact value is 4√7.

What is the largest perfect square that divides 112?

16 = 4². Dividing gives 112 ÷ 16 = 7, and 7 has no square factor left, so √112 = √16 × √7 = 4√7.

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