Question

Without using a calculator, order the following expressions from least to greatest.

Answer 1

Answer:

$\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}$

Step-by-step explanation:

( 1 ) 11/3

$\displaystyle \large{\frac{11}{3}}$ can be converted to mixed fractions to $\displaystyle \large{3\frac{2}{3}}$

Therefore, 11/3 is at least around 3, almost 4. It could be more than 3.5 by approximation but not exactly 4.

( 2 ) √20

$\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 4}}\\\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 2\cdot 2}}\\\displaystyle \large{\sqrt{20}=2\sqrt{5}}$

We know that $\displaystyle \large{\sqrt{4}=2}$ so $\displaystyle \large{\sqrt{5} > \sqrt{4}}$ which means approximately, $\displaystyle \large{\sqrt{20}}$ can be either at least 4.3 up to 4.4

( 3 ) √17

We know that $\displaystyle \large{\sqrt{16} = 4}$ so $\displaystyle \large{\sqrt{17}}$ can be at least 4.1 up to 4.2, but it’s obvious that the square root of 17 is less than square root of 20 since $\displaystyle \large{\sqrt{a} > \sqrt{b}}$ for a > b

Hence, from least to greatest:

$\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}$