Square Root of 152 Simplified

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What is the square root of 152 simplified?

Answer

√152 = 2√38

152 = 4 × 38, and 4 = 2² is the largest perfect square that divides 152, so √152 = √4 × √38 = 2√38. Check: 2√38 ≈ 12.329, the same as √152 ≈ 12.329.

Simplifying √152 Step by Step

1. Prime factorization. — All Prime Factors of 152:

152 = 2 × 2 × 2 × 19 = 23 × 19

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 152Comes out of the rootStays under the root
2322
191—19

3. Take the pairs out of the root.

√152 = √((2 × 2) × 2 × 19)

= 2 × √(2 × 19)

= 2√38

4. Check by squaring back.

2² × 38 = 4 × 38 = 152

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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 152 simplified? (The answer is: 2√38). Enter a whole number (e.g. '152') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
151√151≈ 12.288
1522√38≈ 12.329
1533√17≈ 12.369
154√154≈ 12.41
155√155≈ 12.45
1562√39≈ 12.49
157√157≈ 12.53
158√158≈ 12.57
159√159≈ 12.61
1604√10≈ 12.649
161√161≈ 12.689
1629√2≈ 12.728
163√163≈ 12.767
1642√41≈ 12.806
165√165≈ 12.845
166√166≈ 12.884

FAQ

What is the square root of 152 simplified?

√152 = 2√38

Is 152 a perfect square?

No. 152 = 4 × 38: its largest perfect square factor is 4 = 2², and the factor 38 stays under the radical, so √152 = 2√38.

What is √152 as a decimal?

√152 ≈ 12.329. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√38.

What is the largest perfect square that divides 152?

4 = 2². Dividing gives 152 ÷ 4 = 38, and 38 has no square factor left, so √152 = √4 × √38 = 2√38.

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