Square Root of 148 Simplified

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What is the square root of 148 simplified?

Answer

√148 = 2√37

148 = 4 × 37, and 4 = 2² is the largest perfect square that divides 148, so √148 = √4 × √37 = 2√37. Check: 2√37 ≈ 12.166, the same as √148 ≈ 12.166.

Simplifying √148 Step by Step

1. Prime factorization. — All Prime Factors of 148:

148 = 2 × 2 × 37 = 22 × 37

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 148Comes out of the rootStays under the root
222—
371—37

3. Take the pairs out of the root.

√148 = √((2 × 2) × 37)

= 2 × √37

= 2√37

4. Check by squaring back.

2² × 37 = 4 × 37 = 148

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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 148 simplified? (The answer is: 2√37). Enter a whole number (e.g. '148') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
133√133≈ 11.533
134√134≈ 11.576
1353√15≈ 11.619
1362√34≈ 11.662
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

FAQ

What is the square root of 148 simplified?

√148 = 2√37

Is 148 a perfect square?

No. 148 = 4 × 37: its largest perfect square factor is 4 = 2², and the factor 37 stays under the radical, so √148 = 2√37.

What is √148 as a decimal?

√148 ≈ 12.166. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√37.

What is the largest perfect square that divides 148?

4 = 2². Dividing gives 148 ÷ 4 = 37, and 37 has no square factor left, so √148 = √4 × √37 = 2√37.

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