Question

Match the cube roots for the following numbers.

• A. 11
• B. 9
• C. 8
• D. 7

Answer 1

$1.\Rightarrow \sqrt[3]{3729}$
$=\sqrt[3]{33\times 243}$
$=\sqrt[3]{33\times 3\times 81}$
$=\sqrt[3]{33\times 3\times 3\times 27}$
$=\sqrt[3]{33\times 3\times 3\times 3\times 9}$
​​​​​​​$=\sqrt[3]{3(3\times 3)\times (3\times 3)\times (3\times 3)}$
$=\sqrt[3]{39\times 9\times 9}$
$=9$

$2.\Rightarrow \sqrt[3]{3512}$
$=\sqrt[3]{32\times 256}$
$=\sqrt[3]{32\times 2\times 128}$
​​​​​​​$=\sqrt[3]{32\times 2\times 2\times 64}$
​​​​​​​$=\sqrt[3]{32\times 2\times 2\times 2\times 32}$
​​​​​​​$=\sqrt[3]{32\times 2\times 2\times 2\times 2\times 16}$
​​​​​​​$=\sqrt[3]{3(2\times 2\times 2)\times (2\times 2\times 2)\times 8}$
$=\sqrt[3]{38\times 8\times 8}$
$=8$

$3.\Rightarrow \sqrt[3]{31331}$
$=\sqrt[3]{311\times 121}$
$=\sqrt[3]{3(11\times 11\times 11)}$
$=11$

$4.\Rightarrow \sqrt[3]{3343}$
$=\sqrt[3]{37\times 49}$
$=\sqrt[3]{37\times 7\times 7}$
$=7$