Homework help with simplifying radicals.?

Question

i need help with these.

1) 4 square root 50.

2) square root 2 over 3.

3) square root 24 over square root 2.

can you please help me ?

Answer 1

1. 4 radical 50, well, simplify the radical into all primes: 4 radical 2 x 5 x 5.

You see there's a pair of 5s, take it out and times 5 to 4. Your final answer is 20 radical 2.

2. If you are talking about radical 2/3 I can help you, if you are saying radical 2 over a regular 3, then it's already simplified. For radical 2/3, you times the top and bottom of the fraction with radical 3. You end up with radical 6 over 3.

3. radical 24 over radical 2, times the top and bottom by radical 2, you end up with radical 48 over 2, radical 48 can be simplified to radical 16 x 3, simplify it to 4 radical 3. You final answer is 4 radical 3 over regular 2.

Answer 2

4√50 = 4√(5*5*2) = 20√2

√2 / 3 = √2 / 3

(√24 / √2) = (√(2*2*3*2) / √2) = (2√2√3 / √2) = 2√3

Answer 3

1) 4rt(50)

=4rt(25)rt(2)

=4(5)rt(2)

=20rt(2)

2)

rt(2)/3 is it

If you meant rt(2/3), then

rt(2/3)=rt(2) / rt(3)

=rt(2)rt(3) / rt(3)rt(3) I multiplied top & bottom by rt(3)

=rt(6)/3

3.rt(24)/rt(2)

=rt(12)rt(2)/ rt(2)

=rt(12)

=rt(4)rt(3)

=2rt(3)