Between what two consecutive integers do $sqrt650$ lie?

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Answer 1 · 2015-10-17T04:15:14

$sqrt650$ lies between $25$ and $26$

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 $26$

Between what two consecutive integers do sqrt650sqrt650 lie?