Square Root of 275 Simplified

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What is the square root of 275 simplified?

Answer

√275 = 5√11

275 = 25 × 11, and 25 = 5² is the largest perfect square that divides 275, so √275 = √25 × √11 = 5√11. Check: 5√11 ≈ 16.583, the same as √275 ≈ 16.583.

Simplifying √275 Step by Step

1. Prime factorization. — All Prime Factors of 275:

275 = 5 × 5 × 11 = 52 × 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 275Comes out of the rootStays under the root
525—
111—11

3. Take the pairs out of the root.

√275 = √((5 × 5) × 11)

= 5 × √11

= 5√11

4. Check by squaring back.

5² × 11 = 25 × 11 = 275

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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 275 simplified? (The answer is: 5√11). Enter a whole number (e.g. '275') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
2602√65≈ 16.125
2613√29≈ 16.155
262√262≈ 16.186
263√263≈ 16.217
2642√66≈ 16.248
265√265≈ 16.279
266√266≈ 16.31
267√267≈ 16.34
2682√67≈ 16.371
269√269≈ 16.401
2703√30≈ 16.432
271√271≈ 16.462
2724√17≈ 16.492
273√273≈ 16.523
274√274≈ 16.553
2755√11≈ 16.583
2762√69≈ 16.613
277√277≈ 16.643
278√278≈ 16.673
2793√31≈ 16.703
2802√70≈ 16.733
281√281≈ 16.763
282√282≈ 16.793
283√283≈ 16.823
2842√71≈ 16.852
285√285≈ 16.882
286√286≈ 16.912
287√287≈ 16.941
28812√2≈ 16.971
2891717

FAQ

What is the square root of 275 simplified?

√275 = 5√11

Is 275 a perfect square?

No. 275 = 25 × 11: its largest perfect square factor is 25 = 5², and the factor 11 stays under the radical, so √275 = 5√11.

What is √275 as a decimal?

√275 ≈ 16.583. The decimal never ends and never repeats, so it is always rounded; the exact value is 5√11.

What is the largest perfect square that divides 275?

25 = 5². Dividing gives 275 ÷ 25 = 11, and 11 has no square factor left, so √275 = √25 × √11 = 5√11.

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