Square Root of 270 Simplified

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What is the square root of 270 simplified?

Answer

√270 = 3√30

270 = 9 × 30, and 9 = 3² is the largest perfect square that divides 270, so √270 = √9 × √30 = 3√30. Check: 3√30 ≈ 16.432, the same as √270 ≈ 16.432.

Simplifying √270 Step by Step

1. Prime factorization. — All Prime Factors of 270:

270 = 2 × 3 × 3 × 3 × 5 = 2 × 33 × 5

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 270Comes out of the rootStays under the root
21—2
3333
51—5

3. Take the pairs out of the root.

√270 = √((3 × 3) × 2 × 3 × 5)

= 3 × √(2 × 3 × 5)

= 3√30

4. Check by squaring back.

3² × 30 = 9 × 30 = 270

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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 270 simplified? (The answer is: 3√30). Enter a whole number (e.g. '270') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
2793√31≈ 16.703
2802√70≈ 16.733
281√281≈ 16.763
282√282≈ 16.793
283√283≈ 16.823
2842√71≈ 16.852

FAQ

What is the square root of 270 simplified?

√270 = 3√30

Is 270 a perfect square?

No. 270 = 9 × 30: its largest perfect square factor is 9 = 3², and the factor 30 stays under the radical, so √270 = 3√30.

What is √270 as a decimal?

√270 ≈ 16.432. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√30.

What is the largest perfect square that divides 270?

9 = 3². Dividing gives 270 ÷ 9 = 30, and 30 has no square factor left, so √270 = √9 × √30 = 3√30.

See Also