Dividing Radicals
I used this for the redial sign \/
Problem:
30 \/15
_______
4 \/10
The book says the answer is 15/4 \/6 (15/4 with radicand of 6). I have tried to solve the problem several different ways. I do not arrive at this answer.
how about this :
30√15 / (4√10)
= 15√3 / 2√5 now multiply top and bottom by √2
= 15√6 /4
Thank you for your response.
I did get 15\/3 and 2\/5. Why would you then mutiply by \/2?
The answer in the book is 15/4 with radicand of 4 not a radicand of 6. Are you also showing that there is a missprint in the book and the racdicand is 4?
I have several missprints int he book.
At the top of your post you said the book answer was 15/4 with radicand of 6
and now you say it is 15/4 with radicand of 4 not a radicand of 6. ???
It is generally considered "poor form" to have a radical in the denominator
This goes back to pre-calculator times.
What would you rather have done back in 1950:
divide by √2 which would be dividing by 1.4142136...
or divide by 4 ?
BTW, I just noticed that my second last line in my solution is
15√3 / 2√5
that should have been
15√3 / 2√2
If is 4 \/10. Why would it be 2 \/2 and not the 2 \/5?
OK, from the start:
30√15 / (4√10) divide top and bottom by 2√5
= 15√3 / 2√2 multiply top and bottom by √2
= 15√6 /4
To divide radicals, we can simplify the expression by rationalizing the denominator. Rationalizing the denominator means getting rid of the radicals in the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
In this case, we have:
(30 √15) / (4 √10)
To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator, which is (4 √10):
[(30 √15) / (4 √10)] * [(4 √10) / (4 √10)]
Multiplying numerators and denominators:
(30 * 4 √15 * √10) / (4 * 4 * √10 * √10)
Simplifying:
120 √(15 * 10) / (16 * 10)
120 √(150) / 160
Now, let's simplify the radical:
120 √(5 * 5 * 2 * 3) / 160
120 * 5 * √(2 * 3) / 160
Simplifying the square roots:
600 √(6) / 160
Simplifying the fraction:
3 √6 / (160 / 600)
3 √6 / (3 / 10)
Multiplying the fraction by the reciprocal:
(3 √6) * (10 / 3)
Simplifying:
10 √6
So, the final answer is 10 √6.
It seems that the answer given in the book, which is 15/4 √6, is incorrect.