√52 =
2√13
≈ 7.211103
Square root of 52 — 7.211103 (2√13)
Irrational
The square root of 52 is about 7.211103, or exactly 2√13. It lies between 7 and 8.
- As a decimal
- ≈ 7.211103
- Simplified surd
- √52 = 2√13
- Between
- 7 < √52 < 8
- Squared
- 52² = 2704
- Cube root
- ∛52 ≈ 3.732511
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.
√52 = √(4 × 13) = 2√13
Nearby numbers
From 1 to 200
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200
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 52?
About 7.211103, or exactly 2√13.
Q. Can the surd be simplified?
Yes: 52 = 4 × 13, so 2 comes out and it becomes 2√13.
Q. Between which integers does it fall?
Between 7 and 8.
Q. What is the cube root of 52?
About 3.732511.