Question

Find the cube root of the following number by prime factorization method. identify which given numbers are perfect cubes. a. 729 b. 5832 c. 1944 d. 2744 e. -4096 f. 1323 g. -9276 h. 10648 I. 13824 j. 0.064 k. 0.216 l. 2.744 m. 1.728 n. 512/3375 o. 1 331/1000

please give this answer fast, with pics if possible​

Answer 1

Explanation:

a) 729 = 3 * 3 * 3 * 3 * 3 * 3

`\sqrt[3]{729}=\sqrt[3]{3*3*3*3*3*3}=3*3 = 9`

b) 5832 = 2 * 2 * 2 * 3*3* 3 * 3 * 3 * 3

`\sqrt[3]{5832}=\sqrt[3]{2*2*2* 3*3*3 *3*3*3}=2*3*3 = 18`

`j) 0.064= (64)/(1000)=(2*2*2*2*2*2)/(2*2*2*5*5*5)\\\\\\\sqrt[3]{0.064}=\sqrt[3]{(2*2*2* 2*2*2)/(2*2*2 *5*5*5)}= (2*2)/(2*5)=(4)/(10)=0.4`

`n) \sqrt[3]{(512)/(3375)}=\sqrt[3]{(2*2*2*2*2*2*2*2*2)/(5*5*5*3*3*3)}=(2*2*2)/(5*3)=(8)/(15)`