Square Root of 64 Simplified

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What is the square root of 64 simplified?

Answer

√64 = 8

64 is a perfect square — 64 = 8², so no radical remains: √64 = 8.

Simplifying √64 Step by Step

1. Prime factorization. — All Prime Factors of 64:

64 = 2 × 2 × 2 × 2 × 2 × 2 = 26

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 64Comes out of the rootStays under the root
2623—

3. Take the pairs out of the root.

√64 = √((2 × 2) × (2 × 2) × (2 × 2))

= 2 × 2 × 2

= 8

4. Check by squaring back.

8² = 8 × 8 = 64

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Simplify Square Root Calculator

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 64 simplified? (The answer is: 8). Enter a whole number (e.g. '64') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
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

FAQ

What is the square root of 64 simplified?

√64 = 8

Is 64 a perfect square?

Yes: 64 = 8², so √64 = 8 exactly and nothing stays under the radical.

What is √64 as a decimal?

√64 = 8 exactly — a whole number, because 64 is a perfect square.

What is the largest perfect square that divides 64?

64 itself: it is 8², so √64 = 8.

See Also