Square Root of 164 Simplified

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What is the square root of 164 simplified?

Answer

√164 = 2√41

164 = 4 × 41, and 4 = 2² is the largest perfect square that divides 164, so √164 = √4 × √41 = 2√41. Check: 2√41 ≈ 12.806, the same as √164 ≈ 12.806.

Simplifying √164 Step by Step

1. Prime factorization. — All Prime Factors of 164:

164 = 2 × 2 × 41 = 22 × 41

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 164Comes out of the rootStays under the root
222—
411—41

3. Take the pairs out of the root.

√164 = √((2 × 2) × 41)

= 2 × √41

= 2√41

4. Check by squaring back.

2² × 41 = 4 × 41 = 164

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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 164 simplified? (The answer is: 2√41). Enter a whole number (e.g. '164') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
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

FAQ

What is the square root of 164 simplified?

√164 = 2√41

Is 164 a perfect square?

No. 164 = 4 × 41: its largest perfect square factor is 4 = 2², and the factor 41 stays under the radical, so √164 = 2√41.

What is √164 as a decimal?

√164 ≈ 12.806. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√41.

What is the largest perfect square that divides 164?

4 = 2². Dividing gives 164 ÷ 4 = 41, and 41 has no square factor left, so √164 = √4 × √41 = 2√41.

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