Square roots·√113
√113 =
√113
≈ 10.630146

Square root of 113 — 10.630146 (√113)

Irrational

The square root of 113 is about 10.630146, or exactly √113. It lies between 10 and 11.

As a decimal
≈ 10.630146
Simplified surd
√113 = √113
Between
10 < √113 < 11
Squared
113² = 12769
Cube root
∛113 ≈ 4.834588

Nearby numbers

√110 = √110√111 = √111√112 = 4√7√114 = √114√115 = √115√116 = 2√29

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 113?

About 10.630146, or exactly √113.

Q. Can the surd be simplified?

No — there is no square factor to pull out.

Q. Between which integers does it fall?

Between 10 and 11.

Q. What is the cube root of 113?

About 4.834588.