Square root of 131 lies between which two numbers?

Hint: For solving this question, we need to first convert the data given into an equation. Square root of a number is nothing but a number which produces a specified number when multiplied by itself. It can be rational as well as irrational. We can find the range of squares immediately greater than and less than 131 and use it to find the two numbers between which the square root of 131 lies.

Complete step-by-step answer:
We are given a number 131 and we have to find the two numbers between which the square root lies. To solve this question, we can write the squares of numbers from 1 until we find a square which is greater than 131.
${1^2} = 1$
${2^2} = 4$
${3^2} = 9$
${4^2} = 16$
${5^2} = 25$
${6^2} = 36$
${7^2} = 49$
${8^2} = 64$
${9^2} = 81$
${10^2} = 100$
${11^2} = 121$
${12^2} = 144$
Now since we came across 144 which is greater than 131, we stop.
We know that: $121 < 131 < 144$
Therefore, by applying square root we get;
${(121)^{0.5}} < {(131)^{0.5}} < {(144)^{0.5}}$
By further simplifying the above equation, we get:
$11 < {(131)^{0.5}} < 12$
Therefore, from the above equation we can clearly infer that the square root of 131 lies between 11 and 12.
If in the question they asked the range of integers then the there would be two pairs:
$(11,12)$ and $( - 12, - 11)$.

Note: The most important step in solving a question is converting the data given in the question into a diagram or an equation (depending upon the type of the question). While reading the question, one should be able to understand and write an equation based on the data given. After forming the equation, the simplification is very easy and fast. This knowledge can be extended to solve other complex equations and also cube roots.