are these answers right?
1. �ã-121 =
i�ã11
2. -2�ã-144 =
2i�ã144 =
2i*12=24i
3. �ã-75 =
i=�ã75 =
i�ã5sq*3 =
5i�ã3
4. 5�ã�ã-27 =
5i�ã27 =
5i�ã3sq*3 =
15i�ã3
what about
5. �ã-6 * �ã2 = ??
I will assume that your ã was supposed to come out as √
I disagree with #2
-2√-144
= -2i√144
= -2i(12)
=-24i (you lost the negative sign)
Also I will assume that in#4, the double square root was a typo
If so, then the rest were correct.
#5
√-6√2
= i√12
= 2i√3
yes to #4 i don't know how they symbols don't come out when i type them one way.
Can you help with #5? I didn't get it.
Thank you.
sorry, i see #5 THANK YOU!
If you are on a Mac...
hold down the "Option" key and press V, then release to get the √
There are a whole bunch of those shortcuts, like hold down the "Option" key, and press p to get π
on a PC , I hold down the Alt key, and while holding it down, pres 251 on the number pad, then release. You should get a √ sign
Again just like on a Mac, you can experiment with these on a PC to get different symbols
e.g. try "Alt" 241 to get ±
±âˆš
To verify if the answers are correct, let's go through the steps for each question:
1. √(-121) = √(11^2) = 11
- The answer is correct.
2. -2√(-144) = 2i√(144) = 2i*12 = 24i
- The answer is correct.
3. √(-75) = √(√(75)^2) = √(5^2√3^2) = 5√3
- The answer is correct.
4. 5√(√(-27)) = 5√(√(27)^2) = 5√(3^2√3^2) = 15√3
- The answer is correct.
Now, let's solve the new question:
5. √(-6) * √2 = ?
To multiply square roots, you can multiply the numbers inside the radicals and simplify if possible. If there is an imaginary unit (i) present, you can also multiply them. Let's apply this to the question:
√(-6) * √2 = √(-6 * 2)
= √(-12)
Since there is no natural number whose square is -12, we are left with an irrational answer.
Hence, we can simplify it as:
√(-12) = √((-1) * 12)
= √(-1) * √(12)
= i√12
= i * √(4 * 3)
= i * 2√3
= 2i√3
So, √(-6) * √2 = 2i√3 is the solution.
Please note that square roots of negative numbers involve complex numbers (introduced by the presence of "i" or the imaginary unit), indicating that the result is not a real number.