Square Root of 550 Simplified

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What is the square root of 550 simplified?

Answer

√550 = 5√22

550 = 25 × 22, and 25 = 5² is the largest perfect square that divides 550, so √550 = √25 × √22 = 5√22. Check: 5√22 ≈ 23.452, the same as √550 ≈ 23.452.

Simplifying √550 Step by Step

1. Prime factorization. — All Prime Factors of 550:

550 = 2 × 5 × 5 × 11 = 2 × 52 × 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 550Comes out of the rootStays under the root
21—2
525—
111—11

3. Take the pairs out of the root.

√550 = √((5 × 5) × 2 × 11)

= 5 × √(2 × 11)

= 5√22

4. Check by squaring back.

5² × 22 = 25 × 22 = 550

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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 550 simplified? (The answer is: 5√22). Enter a whole number (e.g. '550') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
50010√5≈ 22.361
50713√3≈ 22.517
514√514≈ 22.672
5255√21≈ 22.913
5284√33≈ 22.978
5505√22≈ 23.452
60010√6≈ 24.495
67515√3≈ 25.981
72012√5≈ 26.833
7255√29≈ 26.926
72611√6≈ 26.944
7292727
7505√30≈ 27.386
7566√21≈ 27.495
7722√193≈ 27.785
7802√195≈ 27.928
80020√2≈ 28.284
8505√34≈ 29.155
8755√35≈ 29.58
8804√55≈ 29.665

FAQ

What is the square root of 550 simplified?

√550 = 5√22

Is 550 a perfect square?

No. 550 = 25 × 22: its largest perfect square factor is 25 = 5², and the factor 22 stays under the radical, so √550 = 5√22.

What is √550 as a decimal?

√550 ≈ 23.452. The decimal never ends and never repeats, so it is always rounded; the exact value is 5√22.

What is the largest perfect square that divides 550?

25 = 5². Dividing gives 550 ÷ 25 = 22, and 22 has no square factor left, so √550 = √25 × √22 = 5√22.

See Also