Square Root of 276 Simplified

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What is the square root of 276 simplified?

Answer

√276 = 2√69

276 = 4 × 69, and 4 = 2² is the largest perfect square that divides 276, so √276 = √4 × √69 = 2√69. Check: 2√69 ≈ 16.613, the same as √276 ≈ 16.613.

Simplifying √276 Step by Step

1. Prime factorization. — All Prime Factors of 276:

276 = 2 × 2 × 3 × 23 = 22 × 3 × 23

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 276Comes out of the rootStays under the root
222—
31—3
231—23

3. Take the pairs out of the root.

√276 = √((2 × 2) × 3 × 23)

= 2 × √(3 × 23)

= 2√69

4. Check by squaring back.

2² × 69 = 4 × 69 = 276

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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 276 simplified? (The answer is: 2√69). Enter a whole number (e.g. '276') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
290√290≈ 17.029

FAQ

What is the square root of 276 simplified?

√276 = 2√69

Is 276 a perfect square?

No. 276 = 4 × 69: its largest perfect square factor is 4 = 2², and the factor 69 stays under the radical, so √276 = 2√69.

What is √276 as a decimal?

√276 ≈ 16.613. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√69.

What is the largest perfect square that divides 276?

4 = 2². Dividing gives 276 ÷ 4 = 69, and 69 has no square factor left, so √276 = √4 × √69 = 2√69.

See Also