√72 =
6√2
≈ 8.485281
Square root of 72 — 8.485281 (6√2)
Irrational
The square root of 72 is about 8.485281, or exactly 6√2. It lies between 8 and 9.
- As a decimal
- ≈ 8.485281
- Simplified surd
- √72 = 6√2
- Between
- 8 < √72 < 9
- Squared
- 72² = 5184
- Cube root
- ∛72 ≈ 4.160168
How the surd is simplified
Pull out the largest square factor. Since 50 = 25 × 2, the root of 25 comes out as 5 and the 2 stays behind: 5√2.
√72 = √(36 × 2) = 6√2
Nearby numbers
From 1 to 200
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How to read this
- The decimal is rounded; the surd form is the exact value.
- Pulling out a square factor simplifies the surd — √50 = 5√2.
- If the number is not a perfect square, the decimal never ends (irrational).
- Knowing which two integers it sits between is enough to estimate in your head.
Frequently asked questions
Q. What is the square root of 72?
About 8.485281, or exactly 6√2.
Q. Can the surd be simplified?
Yes: 72 = 36 × 2, so 6 comes out and it becomes 6√2.
Q. Between which integers does it fall?
Between 8 and 9.
Q. What is the cube root of 72?
About 4.160168.