Square Root of 188 Simplified

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What is the square root of 188 simplified?

Answer

√188 = 2√47

188 = 4 × 47, and 4 = 2² is the largest perfect square that divides 188, so √188 = √4 × √47 = 2√47. Check: 2√47 ≈ 13.711, the same as √188 ≈ 13.711.

Simplifying √188 Step by Step

1. Prime factorization. — All Prime Factors of 188:

188 = 2 × 2 × 47 = 22 × 47

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 188Comes out of the rootStays under the root
222—
471—47

3. Take the pairs out of the root.

√188 = √((2 × 2) × 47)

= 2 × √47

= 2√47

4. Check by squaring back.

2² × 47 = 4 × 47 = 188

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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 188 simplified? (The answer is: 2√47). Enter a whole number (e.g. '188') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
186√186≈ 13.638
187√187≈ 13.675
1882√47≈ 13.711
1893√21≈ 13.748
190√190≈ 13.784
191√191≈ 13.82
1928√3≈ 13.856
193√193≈ 13.892
194√194≈ 13.928
195√195≈ 13.964
1961414
197√197≈ 14.036
1983√22≈ 14.071
199√199≈ 14.107
20010√2≈ 14.142
201√201≈ 14.177
202√202≈ 14.213

FAQ

What is the square root of 188 simplified?

√188 = 2√47

Is 188 a perfect square?

No. 188 = 4 × 47: its largest perfect square factor is 4 = 2², and the factor 47 stays under the radical, so √188 = 2√47.

What is √188 as a decimal?

√188 ≈ 13.711. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√47.

What is the largest perfect square that divides 188?

4 = 2². Dividing gives 188 ÷ 4 = 47, and 47 has no square factor left, so √188 = √4 × √47 = 2√47.

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