Question

Find the cube root of each of the following numbers:
1.) $8\times 64$

2.) $(-216)\times 1728$

3.) $27\times (-2744)$

4.) $(-125)\times (-3375)$

Answer 1

1.) $8\times 64=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

$\sqrt[3]{38\times 64}=2\times 2\times 2=8$ -----(1 mark)

2.) $216\times 1728=2\times 2\times 2\times 3\times 3\times 3\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$

$\sqrt[3]{3(-216)\times 1728}=-(2\times 3\times 2\times 2\times 3)=-72$ -----(1 mark)


3.) $27\times 2744=3\times 3\times 3\times 2\times 2\times 2\times 7\times 7\times 7$

$\sqrt[3]{327\times (-2744)}=-(3\times 2\times 7)=-42$
-----(1 mark)

4.) $125\times 3375=5\times 5\times 5\times 3\times 3\times 3\times 5\times 5\times 5$

$\sqrt[3]{3(-125)\times (-3375)}=5\times 3\times 5=75$
-----(1 mark)