Square Root of 243 Simplified

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What is the square root of 243 simplified?

Answer

√243 = 9√3

243 = 81 × 3, and 81 = 9² is the largest perfect square that divides 243, so √243 = √81 × √3 = 9√3. Check: 9√3 ≈ 15.588, the same as √243 ≈ 15.588.

Simplifying √243 Step by Step

1. Prime factorization. — All Prime Factors of 243:

243 = 3 × 3 × 3 × 3 × 3 = 35

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 243Comes out of the rootStays under the root
35323

3. Take the pairs out of the root.

√243 = √((3 × 3) × (3 × 3) × 3)

= 3 × 3 × √3

= 9√3

4. Check by squaring back.

9² × 3 = 81 × 3 = 243

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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 243 simplified? (The answer is: 9√3). Enter a whole number (e.g. '243') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
249√249≈ 15.78
2505√10≈ 15.811
251√251≈ 15.843
2526√7≈ 15.875
253√253≈ 15.906
254√254≈ 15.937
255√255≈ 15.969
2561616
257√257≈ 16.031

FAQ

What is the square root of 243 simplified?

√243 = 9√3

Is 243 a perfect square?

No. 243 = 81 × 3: its largest perfect square factor is 81 = 9², and the factor 3 stays under the radical, so √243 = 9√3.

What is √243 as a decimal?

√243 ≈ 15.588. The decimal never ends and never repeats, so it is always rounded; the exact value is 9√3.

What is the largest perfect square that divides 243?

81 = 9². Dividing gives 243 ÷ 81 = 3, and 3 has no square factor left, so √243 = √81 × √3 = 9√3.

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