Square Root of 54 Simplified

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What is the square root of 54 simplified?

Answer

√54 = 3√6

54 = 9 × 6, and 9 = 3² is the largest perfect square that divides 54, so √54 = √9 × √6 = 3√6. Check: 3√6 ≈ 7.348, the same as √54 ≈ 7.348.

Simplifying √54 Step by Step

1. Prime factorization. — All Prime Factors of 54:

54 = 2 × 3 × 3 × 3 = 2 × 33

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 54Comes out of the rootStays under the root
21—2
3333

3. Take the pairs out of the root.

√54 = √((3 × 3) × 2 × 3)

= 3 × √(2 × 3)

= 3√6

4. Check by squaring back.

3² × 6 = 9 × 6 = 54

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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 54 simplified? (The answer is: 3√6). Enter a whole number (e.g. '54') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
39√39≈ 6.245
402√10≈ 6.325
41√41≈ 6.403
42√42≈ 6.481
43√43≈ 6.557
442√11≈ 6.633
453√5≈ 6.708
46√46≈ 6.782
47√47≈ 6.856
484√3≈ 6.928
4977
505√2≈ 7.071
51√51≈ 7.141
522√13≈ 7.211
53√53≈ 7.28
543√6≈ 7.348
55√55≈ 7.416
562√14≈ 7.483
57√57≈ 7.55
58√58≈ 7.616
59√59≈ 7.681
602√15≈ 7.746
61√61≈ 7.81
62√62≈ 7.874
633√7≈ 7.937
6488
65√65≈ 8.062
66√66≈ 8.124
67√67≈ 8.185
682√17≈ 8.246

FAQ

What is the square root of 54 simplified?

√54 = 3√6

Is 54 a perfect square?

No. 54 = 9 × 6: its largest perfect square factor is 9 = 3², and the factor 6 stays under the radical, so √54 = 3√6.

What is √54 as a decimal?

√54 ≈ 7.348. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√6.

What is the largest perfect square that divides 54?

9 = 3². Dividing gives 54 ÷ 9 = 6, and 6 has no square factor left, so √54 = √9 × √6 = 3√6.

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