Square Root of 234 Simplified

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What is the square root of 234 simplified?

Answer

√234 = 3√26

234 = 9 × 26, and 9 = 3² is the largest perfect square that divides 234, so √234 = √9 × √26 = 3√26. Check: 3√26 ≈ 15.297, the same as √234 ≈ 15.297.

Simplifying √234 Step by Step

1. Prime factorization. — All Prime Factors of 234:

234 = 2 × 3 × 3 × 13 = 2 × 32 × 13

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 234Comes out of the rootStays under the root
21—2
323—
131—13

3. Take the pairs out of the root.

√234 = √((3 × 3) × 2 × 13)

= 3 × √(2 × 13)

= 3√26

4. Check by squaring back.

3² × 26 = 9 × 26 = 234

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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 234 simplified? (The answer is: 3√26). Enter a whole number (e.g. '234') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
219√219≈ 14.799
2202√55≈ 14.832
221√221≈ 14.866
222√222≈ 14.9
223√223≈ 14.933
2244√14≈ 14.967
2251515
226√226≈ 15.033
227√227≈ 15.067
2282√57≈ 15.1
229√229≈ 15.133
230√230≈ 15.166
231√231≈ 15.199
2322√58≈ 15.232
233√233≈ 15.264
2343√26≈ 15.297
235√235≈ 15.33
2362√59≈ 15.362
237√237≈ 15.395
238√238≈ 15.427
239√239≈ 15.46
2404√15≈ 15.492
241√241≈ 15.524
24211√2≈ 15.556
2439√3≈ 15.588
2442√61≈ 15.62
2457√5≈ 15.652
246√246≈ 15.684
247√247≈ 15.716
2482√62≈ 15.748

FAQ

What is the square root of 234 simplified?

√234 = 3√26

Is 234 a perfect square?

No. 234 = 9 × 26: its largest perfect square factor is 9 = 3², and the factor 26 stays under the radical, so √234 = 3√26.

What is √234 as a decimal?

√234 ≈ 15.297. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√26.

What is the largest perfect square that divides 234?

9 = 3². Dividing gives 234 ÷ 9 = 26, and 26 has no square factor left, so √234 = √9 × √26 = 3√26.

See Also