Square roots·√48
√48 =
4√3
≈ 6.928203

Square root of 48 — 6.928203 (4√3)

Irrational

The square root of 48 is about 6.928203, or exactly 4√3. It lies between 6 and 7.

As a decimal
≈ 6.928203
Simplified surd
√48 = 4√3
Between
6 < √48 < 7
Squared
48² = 2304
Cube root
∛48 ≈ 3.634241

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.

√48 = √(16 × 3) = 4√3

Nearby numbers

√45 = 3√5√46 = √46√47 = √47√49 = 7√50 = 5√2√51 = √51

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 48?

About 6.928203, or exactly 4√3.

Q. Can the surd be simplified?

Yes: 48 = 16 × 3, so 4 comes out and it becomes 4√3.

Q. Between which integers does it fall?

Between 6 and 7.

Q. What is the cube root of 48?

About 3.634241.