√84 =
2√21
≈ 9.165151
Square root of 84 — 9.165151 (2√21)
Irrational
The square root of 84 is about 9.165151, or exactly 2√21. It lies between 9 and 10.
- As a decimal
- ≈ 9.165151
- Simplified surd
- √84 = 2√21
- Between
- 9 < √84 < 10
- Squared
- 84² = 7056
- Cube root
- ∛84 ≈ 4.379519
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.
√84 = √(4 × 21) = 2√21
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 84?
About 9.165151, or exactly 2√21.
Q. Can the surd be simplified?
Yes: 84 = 4 × 21, so 2 comes out and it becomes 2√21.
Q. Between which integers does it fall?
Between 9 and 10.
Q. What is the cube root of 84?
About 4.379519.