# Approximate the square root of 11 by finding the two consecutive whole numbers that the square root lies between?

Jun 18, 2018

See a solution process below:

#### Explanation:

${1}^{2} = 1 \times 1 = 2$

${2}^{2} = 2 \times 2 = 4$

${3}^{2} = 3 \times 3 = 9$

${4}^{2} = 4 \times 4 = 16$

Therefore, $\sqrt{11}$ lies between $3$ and $4$

Jun 18, 2018

Good guess is:

$\approx 3 \frac{2}{7} \approx 3.29$

#### Explanation:

$\sqrt{9} = 3$
$\sqrt{16} = 4$

Our two consecutive whole numbers are 3,4

So the root must be in the range $3 < \sqrt{11} < 4$

Closer to 3 than 4 because $11 - 9 = 2$ and $16 - 11 = 5$

Since there are 7 numbers between 9 and 16 and we are 2 numbers away from 9 let's guess $3 \frac{2}{7} \approx 3.29$

Pretty good guess, a calculator shows $\sqrt{11} \approx 3.32$