Divide the following radical and simplify the answer.
((-3-2√48))/((14√50-8))
A.(24+210√2+64√3+560√6)/(-9736)
B.(12+105√2+32√3+280√6)/(-4868)
C.(12+105√2+32√3+280√6)/4868
D. (24+210√2+64√3+560√6)/9736
Can someone please help. I did it the first time and put d as my answer, and I got it wrong. I did it again, and now I think it is A.
Please answer as soon as possible. I will appreciate it.
Also, please give me a walk through.
I got A
Thank you Damon. You helped a lot, but can you also explain how you got A as well. If you can't explain, it is alright with me, but I do want an explanation on how to get the answer as well. Thank you though, it will help me.
(-3-2sr48) = (-3 -8sr3)* (70sr2+8)
---------- = --------- * -------
14 sr50-8) = (70sr2-8)* (70sr2+8)
= -210sr2-560sr6-24-64sr3
= ----------------------
= (4900*2) - 64
= 24 +210sr2 +64sr3+560sr6
= -------------------------
-9736
Thank you Damon. I now understand how you got A. I got the answer by doing another way than you did, but i guess we are both right in a way. Your explanation helped me a lot. Thank you again.
You are welcome :)
To divide the given radical expression and simplify the answer, follow these steps:
Step 1: Simplify the radicands (the numbers inside the square roots).
First, simplify the radicand in the numerator:
√48 = √(16 * 3) = √16 * √3 = 4√3
Next, simplify the radicand in the denominator:
√50 = √(25 * 2) = √25 * √2 = 5√2
The expression now becomes:
((-3 - 2 * 4√3)) / (14√2 * 5 - 8)
Step 2: Simplify the expression in the denominator.
Multiply using the distributive property:
14√2 * 5 = 70√2
The expression now becomes:
((-3 - 2 * 4√3)) / (70√2 - 8)
Step 3: Simplify the numerator.
Multiply using the distributive property:
-2 * 4√3 = -8√3
The expression now becomes:
((-3 - 8√3)) / (70√2 - 8)
Step 4: Simplify the denominator further.
Multiply using the distributive property:
70√2 - 8 = 70√2 + (-8)
The expression now becomes:
((-3 - 8√3)) / (70√2 + (-8))
Step 5: Rationalize the denominator.
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is (70√2 + 8).
((-3 - 8√3)) * (70√2 + 8) / (70√2 + 8) * (70√2 + 8)
Simplify the numerator:
((-3 - 8√3)) * (70√2 + 8) = -210√2 + 24 - 560√6 - 64√3
Simplify the denominator:
(70√2 + 8) * (70√2 + 8) = 4900 * 2 + 1120√2 + 1120√2 + 64 = 9800 + 2240√2 + 64
The expression now becomes:
(-210√2 + 24 - 560√6 - 64√3) / (9800 + 2240√2 + 64)
Step 6: Combine like terms and simplify.
Combine the terms with √2:
-210√2 - 560√2 = -770√2
Combine the terms with √6:
-560√6 = -560√6
Combine the constant terms:
24 - 64 = -40
The expression now becomes:
(-770√2 - 560√6 - 64√3 - 40) / (9800 + 2240√2 + 64)
Therefore, the simplified answer is:
(-770√2 - 560√6 - 64√3 - 40) / (9800 + 2240√2 + 64)
Comparing this with the given options:
A. (24 + 210√2 + 64√3 + 560√6) / (-9736)
B. (12 + 105√2 + 32√3 + 280√6) / (-4868)
C. (12 + 105√2 + 32√3 + 280√6) / 4868
D. (24 + 210√2 + 64√3 + 560√6) / 9736
The correct answer is option A.