Question

How do you solve these?

Answer 1

Answer:

Step-by-step explanation:

The first and only rule really is to factor these down to their primes and then apply a very simple rule

For every prime, take out 1 prime for every prime under the root sign that equals the index. The rest are thrown away.

That's very wordy. Let's try and see what it means with an example

Take sqrt(27) The index is 1/2 (square root) That means we need two threes in order to apply the rule.

sqrt(27) = sqrt(3 * 3 * 3 ) For every two primes take out 1 and throw one away.

sqrt(27) = 3 sqrt(3) You can't take out that 3rd 3.

64 = 2 * 2 *2 *2 *2 * 2

4th root 64 =  2*2*2 *2 * 2 *2

for every 4th root, you get to take 1 out and throw three away.

4th root 64 = 2 fourth root (2*2)

4th root 64 = 2 fourth root (4)

- 189 = -  3 * 3 * 3 * 7

cuberoot (- 189) = For every 3 roots, you get to pull 1 out and throw the other two away.

3 cube (- 7) is your answer.

72 = 2 * 2 * 2 * 3 * 3

cube root (72) = 2 cube root(9) You don't have enough threes to do any more than what is done.