Question

Between what two consecutive integers do `sqrt650` lie?

Answer 1

`sqrt650` lies between `25` and `26`

Explanation:

Method 1: First we simplify the expression by prime factorising `650`

`sqrt650=sqrt(5*5*13*2)`

`=5sqrt(26)`

`sqrt26 = color(blue)(5.09`

So, `=5sqrt(26) = 5 xx color(blue)(5.09`

`approx25.495`

It can be observed that `sqrt650` lies between `25` and `26`

Method 2
We can estimate the range of `sqrt650` if we have a good idea of squares of numbers.

• `25^2=625`, from this result we get an idea that `sqrt650` is slightly higher that `25`, so we find `26^2`
• `26^2= 676`

So `sqrt650` lies between `25` and `26`