Square Root of 729 Simplified

Simplify Square Root Calculator
Simplify the square root of

What is the square root of 729 simplified?

Answer

√729 = 27

729 is a perfect square — 729 = 27², so no radical remains: √729 = 27.

Simplifying √729 Step by Step

1. Prime factorization. — All Prime Factors of 729:

729 = 3 × 3 × 3 × 3 × 3 × 3 = 36

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 729Comes out of the rootStays under the root
3633—

3. Take the pairs out of the root.

√729 = √((3 × 3) × (3 × 3) × (3 × 3))

= 3 × 3 × 3

= 27

4. Check by squaring back.

27² = 27 × 27 = 729

Related Calculations

See Also

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 729 simplified? (The answer is: 27). Enter a whole number (e.g. '729') and hit the 'Simplify' button.
Recalculate with different values ↑

Simplified Square Roots Table

NumberSimplest radical formDecimal value
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
97218√3≈ 31.177
1,00010√10≈ 31.623
1,20020√3≈ 34.641
1,25025√2≈ 35.355
1,2606√35≈ 35.496

FAQ

What is the square root of 729 simplified?

√729 = 27

Is 729 a perfect square?

Yes: 729 = 27², so √729 = 27 exactly and nothing stays under the radical.

What is √729 as a decimal?

√729 = 27 exactly — a whole number, because 729 is a perfect square.

What is the largest perfect square that divides 729?

729 itself: it is 27², so √729 = 27.

See Also