# Between what two consecutive integers do sqrt650 lie?

##### 1 Answer
Oct 17, 2015

$\sqrt{650}$ lies between $25$ and $26$

#### Explanation:

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

$\sqrt{650} = \sqrt{5 \cdot 5 \cdot 13 \cdot 2}$

$= 5 \sqrt{26}$

sqrt26 = color(blue)(5.09

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

$\approx 25.495$

It can be observed that $\sqrt{650}$ lies between $25$ and $26$

Method 2
We can estimate the range of $\sqrt{650}$ if we have a good idea of squares of numbers.

• ${25}^{2} = 625$, from this result we get an idea that $\sqrt{650}$ is slightly higher that $25$, so we find ${26}^{2}$
• ${26}^{2} = 676$

So $\sqrt{650}$ lies between $25$ and $26$