√169 = 13, because 13 × 13 = 169
√169 = 13. Thirteen squared has a neat mirror image — and the tens-and-units split works for every square from 11² to 19².
√169 = 13. The square root of a number is whatever you have to multiply by itself to get that number, and 13 × 13 = 169, so 13 is the answer.
169 is a perfect square — it is 13 squared — which means its root is a whole number with nothing left over. Strictly there are two numbers that square to 169, because −13 × −13 = 169 as well, but "the square root of 169" on its own means the positive one: 13.
In words: the square root of one hundred and sixty-nine is thirteen.
Squaring is the way back. 13 × 13 = 169, so the root is right. That check costs one multiplication and catches every slip.
13 × 13 is easiest as (10 + 3)²: 100 + 30 + 30 + 9 = 169. Splitting into tens and units is how every square from 11² to 19² can be done in your head.
Reverse the digits of 13 and of 169 and you get another true fact: 31² = 961. Only a few numbers do this — 12² = 144 and 21² = 441 is the other well-known pair.
169 is also the number of squares in a 13 × 13 grid, and the thirteenth square number, so √169 = 13 is a fact that comes up in grid puzzles and board layouts.
169 lies between 169 (13²) and 196 (14²). Bracketing between the nearest squares is the fastest mental check for any root.
The square root of 169 is 13, because 13 × 13 = 169.
Yes. 169 is 13 squared, so its square root is the whole number 13.
Bracket it between the two nearest square numbers — 169 and 196 — then judge how far along the gap 169 sits. That gets you to roughly 13, which is close enough for almost any mental check.
169 ÷ 13 = 13. Dividing a square number by its square root gives the root straight back, because 13 × 13 = 169.
169 − 13 = 156, which is also 12 × 13 — one thirteen fewer than 13 × 13.
Every square number up to 25² — and the roots people most often look up — is listed on the square numbers page.