Square Root of 171 Simplified

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What is the square root of 171 simplified?

Answer

√171 = 3√19

171 = 9 × 19, and 9 = 3² is the largest perfect square that divides 171, so √171 = √9 × √19 = 3√19. Check: 3√19 ≈ 13.077, the same as √171 ≈ 13.077.

Simplifying √171 Step by Step

1. Prime factorization. — All Prime Factors of 171:

171 = 3 × 3 × 19 = 32 × 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 171Comes out of the rootStays under the root
323—
191—19

3. Take the pairs out of the root.

√171 = √((3 × 3) × 19)

= 3 × √19

= 3√19

4. Check by squaring back.

3² × 19 = 9 × 19 = 171

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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 171 simplified? (The answer is: 3√19). Enter a whole number (e.g. '171') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
167√167≈ 12.923
1682√42≈ 12.961
1691313
170√170≈ 13.038
1713√19≈ 13.077
1722√43≈ 13.115
173√173≈ 13.153
174√174≈ 13.191
1755√7≈ 13.229
1764√11≈ 13.266
177√177≈ 13.304
178√178≈ 13.342
179√179≈ 13.379
1806√5≈ 13.416
181√181≈ 13.454
182√182≈ 13.491
183√183≈ 13.528
1842√46≈ 13.565
185√185≈ 13.601

FAQ

What is the square root of 171 simplified?

√171 = 3√19

Is 171 a perfect square?

No. 171 = 9 × 19: its largest perfect square factor is 9 = 3², and the factor 19 stays under the radical, so √171 = 3√19.

What is √171 as a decimal?

√171 ≈ 13.077. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√19.

What is the largest perfect square that divides 171?

9 = 3². Dividing gives 171 ÷ 9 = 19, and 19 has no square factor left, so √171 = √9 × √19 = 3√19.

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