Square Root of 264 Simplified

Simplify Square Root Calculator
Simplify the square root of

What is the square root of 264 simplified?

Answer

√264 = 2√66

264 = 4 × 66, and 4 = 2² is the largest perfect square that divides 264, so √264 = √4 × √66 = 2√66. Check: 2√66 ≈ 16.248, the same as √264 ≈ 16.248.

Simplifying √264 Step by Step

1. Prime factorization. — All Prime Factors of 264:

264 = 2 × 2 × 2 × 3 × 11 = 23 × 3 × 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 264Comes out of the rootStays under the root
2322
31—3
111—11

3. Take the pairs out of the root.

√264 = √((2 × 2) × 2 × 3 × 11)

= 2 × √(2 × 3 × 11)

= 2√66

4. Check by squaring back.

2² × 66 = 4 × 66 = 264

Related Calculations

See Also

Simplify Square Root Calculator

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 264 simplified? (The answer is: 2√66). Enter a whole number (e.g. '264') and hit the 'Simplify' button.
Recalculate with different values ↑

Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
258√258≈ 16.062
259√259≈ 16.093
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

FAQ

What is the square root of 264 simplified?

√264 = 2√66

Is 264 a perfect square?

No. 264 = 4 × 66: its largest perfect square factor is 4 = 2², and the factor 66 stays under the radical, so √264 = 2√66.

What is √264 as a decimal?

√264 ≈ 16.248. The decimal never ends and never repeats, so it is always rounded; the exact value is 2√66.

What is the largest perfect square that divides 264?

4 = 2². Dividing gives 264 ÷ 4 = 66, and 66 has no square factor left, so √264 = √4 × √66 = 2√66.

See Also