Question

Find all the real cube roots of the number

1.) 1000/27

Find all the real square roots

2.) 0.0625

Find all the real fourth roots

3.) 625

Simplify each radical expressions. Use absolute value symbols when needed.

4.) 3 Radical 64x^9/343

Answer 1

hint, break every term into their prime factorizations to start

Answer 2

How do i do that?

Answer 3

1. 10/3
2. +0.25 and -0.25 are the real square roots

Answer 4

3. ± 5

Answer 5

plus or minus 5 is number 3

Answer 6

How did you get 1 and 2?

Answer 7

4. 4x^9/343

Answer 8

Can you explain how you got the answer to that, please?

Answer 9

2) 625 * 10^-4
take the square root = 25 * 10^-2 = 0.25

Answer 10

square root of the square root is the same as the fourth root
4th root of 625 = square root of 25 = 5

therefore the 4th root of 625= 5

Answer 11

So, may I do a quick assistance here: @mathhasproblems a prime factorization is where you break a number down until you can't anymore, for example 21=3*7 or 45=9*5=3*3*5

Answer 12

for square roots, square implies 2, so you need exactly 2 of the same number in order to pull the number out, for a cube root, cube implies 3, so you need exactly 3 of a number to pull the number out, then it continues

Answer 13

4) 343 can be written as 7^3 64 = 8^2 and 9 = 3^2

Answer 14

here is a quick reference on both topics: http://www.purplemath.com/modules/factnumb.htm
http://www.purplemath.com/modules/radicals.htm

Answer 15

did you mean the cube root for number 4?