Square Root of 198 Simplified

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What is the square root of 198 simplified?

Answer

√198 = 3√22

198 = 9 × 22, and 9 = 3² is the largest perfect square that divides 198, so √198 = √9 × √22 = 3√22. Check: 3√22 ≈ 14.071, the same as √198 ≈ 14.071.

Simplifying √198 Step by Step

1. Prime factorization. — All Prime Factors of 198:

198 = 2 × 3 × 3 × 11 = 2 × 32 × 11

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 198Comes out of the rootStays under the root
21—2
323—
111—11

3. Take the pairs out of the root.

√198 = √((3 × 3) × 2 × 11)

= 3 × √(2 × 11)

= 3√22

4. Check by squaring back.

3² × 22 = 9 × 22 = 198

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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 198 simplified? (The answer is: 3√22). Enter a whole number (e.g. '198') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
203√203≈ 14.248
2042√51≈ 14.283
205√205≈ 14.318
206√206≈ 14.353
2073√23≈ 14.387
2084√13≈ 14.422
209√209≈ 14.457
210√210≈ 14.491
211√211≈ 14.526
2122√53≈ 14.56

FAQ

What is the square root of 198 simplified?

√198 = 3√22

Is 198 a perfect square?

No. 198 = 9 × 22: its largest perfect square factor is 9 = 3², and the factor 22 stays under the radical, so √198 = 3√22.

What is √198 as a decimal?

√198 ≈ 14.071. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√22.

What is the largest perfect square that divides 198?

9 = 3². Dividing gives 198 ÷ 9 = 22, and 22 has no square factor left, so √198 = √9 × √22 = 3√22.

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