Square Root of 298 Simplified

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What is the square root of 298 simplified?

Answer

√298 cannot be simplified — its simplest radical form is
√298

√298 is already in simplest form — 298 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √298 ≈ 17.263.

Simplifying √298 Step by Step

1. Prime factorization. — All Prime Factors of 298:

298 = 2 × 149

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 298Comes out of the rootStays under the root
21—2
1491—149

3. Take the pairs out of the root.

√298 = √(2 × 149)

No prime appears twice, so there is no pair to take out.

√298

4. Check by squaring back.

The only perfect square dividing 298 is 1 = 1², and 1² × 298 = 298

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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 298 simplified? (The answer is: √298). Enter a whole number (e.g. '298') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
4953√55≈ 22.249

FAQ

What is the square root of 298 simplified?

√298 cannot be simplified — its simplest radical form is √298

Is 298 a perfect square?

No. 298 has no perfect square factor other than 1, so √298 cannot be simplified and stays √298.

What is √298 as a decimal?

√298 ≈ 17.263. The decimal never ends and never repeats, so it is always rounded; the exact value is √298.

What is the largest perfect square that divides 298?

Only 1. 298 has no other square factor, so √298 is already in simplest radical form.

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