Square Root of 250 Simplified

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What is the square root of 250 simplified?

Answer

√250 = 5√10

250 = 25 × 10, and 25 = 5² is the largest perfect square that divides 250, so √250 = √25 × √10 = 5√10. Check: 5√10 ≈ 15.811, the same as √250 ≈ 15.811.

Simplifying √250 Step by Step

1. Prime factorization. — All Prime Factors of 250:

250 = 2 × 5 × 5 × 5 = 2 × 53

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 250Comes out of the rootStays under the root
21—2
5355

3. Take the pairs out of the root.

√250 = √((5 × 5) × 2 × 5)

= 5 × √(2 × 5)

= 5√10

4. Check by squaring back.

5² × 10 = 25 × 10 = 250

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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 250 simplified? (The answer is: 5√10). Enter a whole number (e.g. '250') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
235√235≈ 15.33
2362√59≈ 15.362
237√237≈ 15.395
238√238≈ 15.427
239√239≈ 15.46
2404√15≈ 15.492
241√241≈ 15.524
24211√2≈ 15.556
2439√3≈ 15.588
2442√61≈ 15.62
2457√5≈ 15.652
246√246≈ 15.684
247√247≈ 15.716
2482√62≈ 15.748
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

FAQ

What is the square root of 250 simplified?

√250 = 5√10

Is 250 a perfect square?

No. 250 = 25 × 10: its largest perfect square factor is 25 = 5², and the factor 10 stays under the radical, so √250 = 5√10.

What is √250 as a decimal?

√250 ≈ 15.811. The decimal never ends and never repeats, so it is always rounded; the exact value is 5√10.

What is the largest perfect square that divides 250?

25 = 5². Dividing gives 250 ÷ 25 = 10, and 10 has no square factor left, so √250 = √25 × √10 = 5√10.

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