Square Root of 160 Simplified

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What is the square root of 160 simplified?

Answer

√160 = 4√10

160 = 16 × 10, and 16 = 4² is the largest perfect square that divides 160, so √160 = √16 × √10 = 4√10. Check: 4√10 ≈ 12.649, the same as √160 ≈ 12.649.

Simplifying √160 Step by Step

1. Prime factorization. — All Prime Factors of 160:

160 = 2 × 2 × 2 × 2 × 2 × 5 = 25 × 5

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 160Comes out of the rootStays under the root
25222
51—5

3. Take the pairs out of the root.

√160 = √((2 × 2) × (2 × 2) × 2 × 5)

= 2 × 2 × √(2 × 5)

= 4√10

4. Check by squaring back.

4² × 10 = 16 × 10 = 160

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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 160 simplified? (The answer is: 4√10). Enter a whole number (e.g. '160') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
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

FAQ

What is the square root of 160 simplified?

√160 = 4√10

Is 160 a perfect square?

No. 160 = 16 × 10: its largest perfect square factor is 16 = 4², and the factor 10 stays under the radical, so √160 = 4√10.

What is √160 as a decimal?

√160 ≈ 12.649. The decimal never ends and never repeats, so it is always rounded; the exact value is 4√10.

What is the largest perfect square that divides 160?

16 = 4². Dividing gives 160 ÷ 16 = 10, and 10 has no square factor left, so √160 = √16 × √10 = 4√10.

See Also