Square Root of 225 Simplified

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What is the square root of 225 simplified?

Answer

√225 = 15

225 is a perfect square — 225 = 15², so no radical remains: √225 = 15.

Simplifying √225 Step by Step

1. Prime factorization. — All Prime Factors of 225:

225 = 3 × 3 × 5 × 5 = 32 × 52

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 225Comes out of the rootStays under the root
323—
525—

3. Take the pairs out of the root.

√225 = √((3 × 3) × (5 × 5))

= 3 × 5

= 15

4. Check by squaring back.

15² = 15 × 15 = 225

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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 225 simplified? (The answer is: 15). Enter a whole number (e.g. '225') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
210√210≈ 14.491
211√211≈ 14.526
2122√53≈ 14.56
213√213≈ 14.595
214√214≈ 14.629
215√215≈ 14.663
2166√6≈ 14.697
217√217≈ 14.731
218√218≈ 14.765
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

FAQ

What is the square root of 225 simplified?

√225 = 15

Is 225 a perfect square?

Yes: 225 = 15², so √225 = 15 exactly and nothing stays under the radical.

What is √225 as a decimal?

√225 = 15 exactly — a whole number, because 225 is a perfect square.

What is the largest perfect square that divides 225?

225 itself: it is 15², so √225 = 15.

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