Square Root of 800 Simplified

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What is the square root of 800 simplified?

Answer

√800 = 20√2

800 = 400 × 2, and 400 = 20² is the largest perfect square that divides 800, so √800 = √400 × √2 = 20√2. Check: 20√2 ≈ 28.284, the same as √800 ≈ 28.284.

Simplifying √800 Step by Step

1. Prime factorization. — All Prime Factors of 800:

800 = 2 × 2 × 2 × 2 × 2 × 5 × 5 = 25 × 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 800Comes out of the rootStays under the root
25222
525—

3. Take the pairs out of the root.

√800 = √((2 × 2) × (2 × 2) × (5 × 5) × 2)

= 2 × 2 × 5 × √2

= 20√2

4. Check by squaring back.

20² × 2 = 400 × 2 = 800

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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 800 simplified? (The answer is: 20√2). Enter a whole number (e.g. '800') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
97218√3≈ 31.177
1,00010√10≈ 31.623
1,20020√3≈ 34.641
1,25025√2≈ 35.355
1,2606√35≈ 35.496
1,28016√5≈ 35.777
1,2963636
1,57515√7≈ 39.686
1,87525√3≈ 43.301
2,00020√5≈ 44.721

FAQ

What is the square root of 800 simplified?

√800 = 20√2

Is 800 a perfect square?

No. 800 = 400 × 2: its largest perfect square factor is 400 = 20², and the factor 2 stays under the radical, so √800 = 20√2.

What is √800 as a decimal?

√800 ≈ 28.284. The decimal never ends and never repeats, so it is always rounded; the exact value is 20√2.

What is the largest perfect square that divides 800?

400 = 20². Dividing gives 800 ÷ 400 = 2, and 2 has no square factor left, so √800 = √400 × √2 = 20√2.

See Also