Square Root of 169 Simplified

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What is the square root of 169 simplified?

Answer

√169 = 13

169 is a perfect square — 169 = 13², so no radical remains: √169 = 13.

Simplifying √169 Step by Step

1. Prime factorization. — All Prime Factors of 169:

169 = 13 × 13 = 132

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 169Comes out of the rootStays under the root
13213—

3. Take the pairs out of the root.

√169 = √(13 × 13)

= 13

4. Check by squaring back.

13² = 13 × 13 = 169

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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 169 simplified? (The answer is: 13). Enter a whole number (e.g. '169') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
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

FAQ

What is the square root of 169 simplified?

√169 = 13

Is 169 a perfect square?

Yes: 169 = 13², so √169 = 13 exactly and nothing stays under the radical.

What is √169 as a decimal?

√169 = 13 exactly — a whole number, because 169 is a perfect square.

What is the largest perfect square that divides 169?

169 itself: it is 13², so √169 = 13.

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