Square Root of 600 Simplified

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What is the square root of 600 simplified?

Answer

√600 = 10√6

600 = 100 × 6, and 100 = 10² is the largest perfect square that divides 600, so √600 = √100 × √6 = 10√6. Check: 10√6 ≈ 24.495, the same as √600 ≈ 24.495.

Simplifying √600 Step by Step

1. Prime factorization. — All Prime Factors of 600:

600 = 2 × 2 × 2 × 3 × 5 × 5 = 23 × 3 × 52

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 600Comes out of the rootStays under the root
2322
31—3
525—

3. Take the pairs out of the root.

√600 = √((2 × 2) × (5 × 5) × 2 × 3)

= 2 × 5 × √(2 × 3)

= 10√6

4. Check by squaring back.

10² × 6 = 100 × 6 = 600

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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 600 simplified? (The answer is: 10√6). Enter a whole number (e.g. '600') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
9608√15≈ 30.984

FAQ

What is the square root of 600 simplified?

√600 = 10√6

Is 600 a perfect square?

No. 600 = 100 × 6: its largest perfect square factor is 100 = 10², and the factor 6 stays under the radical, so √600 = 10√6.

What is √600 as a decimal?

√600 ≈ 24.495. The decimal never ends and never repeats, so it is always rounded; the exact value is 10√6.

What is the largest perfect square that divides 600?

100 = 10². Dividing gives 600 ÷ 100 = 6, and 6 has no square factor left, so √600 = √100 × √6 = 10√6.

See Also