Square Root of 147 Simplified

Simplify Square Root Calculator
Simplify the square root of

What is the square root of 147 simplified?

Answer

√147 = 7√3

147 = 49 × 3, and 49 = 7² is the largest perfect square that divides 147, so √147 = √49 × √3 = 7√3. Check: 7√3 ≈ 12.124, the same as √147 ≈ 12.124.

Simplifying √147 Step by Step

1. Prime factorization. — All Prime Factors of 147:

147 = 3 × 7 × 7 = 3 × 72

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 147Comes out of the rootStays under the root
31—3
727—

3. Take the pairs out of the root.

√147 = √((7 × 7) × 3)

= 7 × √3

= 7√3

4. Check by squaring back.

7² × 3 = 49 × 3 = 147

Related Calculations

See Also

Simplify Square Root Calculator

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 147 simplified? (The answer is: 7√3). Enter a whole number (e.g. '147') and hit the 'Simplify' button.
Recalculate with different values ↑

Simplified Square Roots Table

NumberSimplest radical formDecimal value
1322√33≈ 11.489
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

FAQ

What is the square root of 147 simplified?

√147 = 7√3

Is 147 a perfect square?

No. 147 = 49 × 3: its largest perfect square factor is 49 = 7², and the factor 3 stays under the radical, so √147 = 7√3.

What is √147 as a decimal?

√147 ≈ 12.124. The decimal never ends and never repeats, so it is always rounded; the exact value is 7√3.

What is the largest perfect square that divides 147?

49 = 7². Dividing gives 147 ÷ 49 = 3, and 3 has no square factor left, so √147 = √49 × √3 = 7√3.

See Also