Square Root of 72 Simplified

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What is the square root of 72 simplified?

Answer

√72 = 6√2

72 = 36 × 2, and 36 = 6² is the largest perfect square that divides 72, so √72 = √36 × √2 = 6√2. Check: 6√2 ≈ 8.485, the same as √72 ≈ 8.485.

Simplifying √72 Step by Step

1. Prime factorization. — All Prime Factors of 72:

72 = 2 × 2 × 2 × 3 × 3 = 23 × 32

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 72Comes out of the rootStays under the root
2322
323—

3. Take the pairs out of the root.

√72 = √((2 × 2) × (3 × 3) × 2)

= 2 × 3 × √2

= 6√2

4. Check by squaring back.

6² × 2 = 36 × 2 = 72

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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 72 simplified? (The answer is: 6√2). Enter a whole number (e.g. '72') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
69√69≈ 8.307
70√70≈ 8.367
71√71≈ 8.426
726√2≈ 8.485
73√73≈ 8.544
74√74≈ 8.602
755√3≈ 8.66
762√19≈ 8.718
77√77≈ 8.775
78√78≈ 8.832
79√79≈ 8.888
804√5≈ 8.944
8199
82√82≈ 9.055
83√83≈ 9.11
842√21≈ 9.165
85√85≈ 9.22
86√86≈ 9.274

FAQ

What is the square root of 72 simplified?

√72 = 6√2

Is 72 a perfect square?

No. 72 = 36 × 2: its largest perfect square factor is 36 = 6², and the factor 2 stays under the radical, so √72 = 6√2.

What is √72 as a decimal?

√72 ≈ 8.485. The decimal never ends and never repeats, so it is always rounded; the exact value is 6√2.

What is the largest perfect square that divides 72?

36 = 6². Dividing gives 72 ÷ 36 = 2, and 2 has no square factor left, so √72 = √36 × √2 = 6√2.

See Also