√ Does NOT make sense, PLEASE EXPLAIN/Anwser PLEASE & CHECK MY WORK?

Question

√ Doesn't make sense.
My question:
1) √15√24√30=

my work: √5*3*√6*4*√15*2= √5*3*2√6*√15*2

2) How come if the √ square root is the opposite of square than how does my √15*2= √30 makes sense? (I cant even simplify it now) THEY DONT HAVE ANYTHING IN COMMON!

3) What is wrong with my: √5*3*2√6*√15*2 ???

I put the 2 outside the radical because it is actually 4 cause 2²=4.

Answer 1

When square roots are multiplied together, you can multiply the numbers first, and then take one square root at the end.

Find prime factors for all the numbers:
15 = 5 * 3
24 = 2^3 * 3
30 = 3 * 5 * 2
Multiplying all these together gives:
2^4 * 3^3 * 5^2

You can now take square roots as follows:
2^4 becomes 2^2
3^3 = 3*(3^2) and becomes 3sqrt(3)
5^2 becomes 5
The end result is 2^2 * 5 * 3 sqrt(3) = 60sqrt(3).

It is not clear when you write sqrt 3 * 2 whether you mean sqrt(3) * 2 or sqrt(3*2).

Answer 2

1) Your objective is to get as many of the same radicals as possible. If the sq rt of anything is multiplied by it's sq rt again, then it just becomes that number. For instance, sqrt.(2) times sqrt.(2) is simply 2. So, for your problem, you were on the right track.

sqrt(5 * 3)sqrt(2*2*2*3)sqrt(5*3*2)

you have two 5's, four 2's, and three 3's. So now let's simplify:

5*2*2*3sqrt(3) = 60sqrt(3)

2. Square root is indeed the opposite of squaring. if you square 60*sqrt(3) and also multiply 15, 24, and 30, you should obtain the same answer. Your sqrt 15 * 2 may be right or wrong, but I'm not sure, because I don't know what you're including under the radical. It works out because if you take sqrt(30) squared, you simply get 30, but if you take sqrt(15)*sqrt(2) and square it, you get 15*2, or 30. You may be pulling constants out of the radical that you are not able to. Breaking apart a radical only results in more radicals, unless they themselves are perfect squares (like 4, 9, 25, etc), which can be simplified to constant integers.

3. If what you wrote was sqrt(5*3)*2sqrt(6)*sqrt(15*2), then there is nothing wrong. However, you need to break down the numbers to their prime factorization to do much with them.

I hope this helps!

Answer 3

√15√24√30 =
√15√24√15√2 =
15√24√2 =
15√48 =
15√16√3 =
60√3

Answer 4

You need to break down the numbers to prime factors
15 is 3*5, 24 is 2*2*2*3, 30 is 5*3*2 put all these numbers under the radical and take out whatever you see a pair off.

SQRT(3*5*2*2*2*3*5*3*2) is
2*2*3*5 sqrt 3
60 sqrt 3

I agree with rackbrain; a math script is in order for this forum

Answer 5

sqrt (15) sqrt(24) sqrt(30)

sqrt(15 x 24 x 30) = sqrt(3x 5) x (6x 4) x (5 x 6)

(reorganized terms) = sqrt (3 x 4) x (5 x5) x (6 x 6)

= sqrt(3) x sqrt(4) x sqrt (25) x sqrt (36)

= (sqrt 3) x 2 x 5 x 6

= 60 sqrt 3