Square Root of 297 Simplified

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What is the square root of 297 simplified?

Answer

√297 = 3√33

297 = 9 × 33, and 9 = 3² is the largest perfect square that divides 297, so √297 = √9 × √33 = 3√33. Check: 3√33 ≈ 17.234, the same as √297 ≈ 17.234.

Simplifying √297 Step by Step

1. Prime factorization. — All Prime Factors of 297:

297 = 3 × 3 × 3 × 11 = 33 × 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 297Comes out of the rootStays under the root
3333
111—11

3. Take the pairs out of the root.

√297 = √((3 × 3) × 3 × 11)

= 3 × √(3 × 11)

= 3√33

4. Check by squaring back.

3² × 33 = 9 × 33 = 297

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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 297 simplified? (The answer is: 3√33). Enter a whole number (e.g. '297') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
291√291≈ 17.059
2922√73≈ 17.088
293√293≈ 17.117
2947√6≈ 17.146
295√295≈ 17.176
2962√74≈ 17.205
2973√33≈ 17.234
298√298≈ 17.263
299√299≈ 17.292
30010√3≈ 17.321
3122√78≈ 17.664
3255√13≈ 18.028
330√330≈ 18.166
36311√3≈ 19.053
3755√15≈ 19.365
385√385≈ 19.621
4002020
4059√5≈ 20.125
43212√3≈ 20.785
45015√2≈ 21.213
4804√30≈ 21.909

FAQ

What is the square root of 297 simplified?

√297 = 3√33

Is 297 a perfect square?

No. 297 = 9 × 33: its largest perfect square factor is 9 = 3², and the factor 33 stays under the radical, so √297 = 3√33.

What is √297 as a decimal?

√297 ≈ 17.234. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√33.

What is the largest perfect square that divides 297?

9 = 3². Dividing gives 297 ÷ 9 = 33, and 33 has no square factor left, so √297 = √9 × √33 = 3√33.

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