Question

Find the cube roots of the following numbers.(1) 8000 (2) 729 (3) 343 (4) -512 (5) -2744 (6) 32768

Answer 1

1) 20
2) 9
3) 7
4)-8
5) -14
6) 32

Answer 2

Answer:

We have to find the cube root of the given numbers

$1). \sqrt[3]{8000} = \sqrt[3]{ \times 5 \times 5 \times 5}\\\sqrt[3]{8000}= \sqrt[3]{4^3 \times 5^3} = \sqrt[3]{(20)^3} \\\sqrt[3]{8000}= \sqrt[3]{20^3} = 20\\ \\2). \sqrt[3]{ 729} = \sqrt[3]{3\times3\times3\times3\times3\times3} \\\sqrt[3]{ 729} = \sqrt[3]{9^3} = 9 \\3).\sqrt[3]{343}=\sqrt[3]{7 \times 7\times7} \\\sqrt[3]{343}= \sqrt[3]{7^3} = 7 \\4). - \sqrt[3]{512 } =- \sqrt[3]{8 \times 8 \times 8} \\- \sqrt[3]{512} = -\sqrt[3]{8^3} = -8$

$5).-\sqrt[3]{2744}=-\sqrt[3{7\times7\times7\times2\times2\times2}\\ -\sqrt[3]{2744} = - \sqrt[3]{7^3 \times 2^3}\\-\sqrt[3]{2744} =-\sqrt[3]{14^3}\\ = -14\\6). \sqrt[3]{32768} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\times 2}\\  \sqrt[3]{32768} = \sqrt[3]{8^3 \times4^3}\\ \sqrt[3]{32768} = \sqrt[3]{32^3} = 32$