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Triptych !!DP4/G/5A6 (OP) replied with this 15 years ago, 2 minutes later, 4 minutes after the original post[^][v]#80,473
@80,471 (C)
"To obtain the positive value of the square root of a number, first express the number in exponential notation in which the power of 10 has an even exponent. To obtain the positive square root of the exponential number, obtain the square root of the decimal from a calculator, and obtain the square root of the power of 10 by dividing the exponent by 2." I don't get why. :<
Anonymous C replied with this 15 years ago, 2 minutes later, 6 minutes after the original post[^][v]#80,475
@previous (Triptych !!DP4/G/5A6)
I thought square roots were always positive unless i was used. Can I get the numbers you're using?
Triptych !!DP4/G/5A6 (OP) replied with this 15 years ago, 5 minutes later, 12 minutes after the original post[^][v]#80,477
@previous (C)
Here's an example problem:
√4.00 * 10^-4 = √4.00 * √10^-4 = 2.00 * 10^-(4/2) = 2.00 * 10^-2
I think the positive bit was just for clarification.
(Edited 39 seconds later.)
Anonymous C replied with this 15 years ago, 3 minutes later, 15 minutes after the original post[^][v]#80,480
@previous (Triptych !!DP4/G/5A6)
just write the exponents as 1/2 and multiply the exponents then solve.
Triptych !!DP4/G/5A6 (OP) replied with this 15 years ago, 43 seconds later, 16 minutes after the original post[^][v]#80,481
@previous (C)
I know how to do it, but why divide the exponent by 2?
Anonymous C replied with this 15 years ago, 1 minute later, 17 minutes after the original post[^][v]#80,483
Anonymous E joined in and replied with this 15 years ago, 20 minutes later, 39 minutes after the original post[^][v]#80,492
@80,475 (C)
The square root could be positive or negative number.
(-2)^2 = 4
(2)^2 = 4
sqrt(4)=+/-2
@80,481 (Triptych !!DP4/G/5A6)
You are dividing by 2 because it is a square root. It is the same as using 1/2 as an exponent. By taking the square root, you are dividing the exponent into two parts that multiply to the original.
10^4 = 10^2 * 10^2 → sqrt(10^4) = 10^2
x^12 = x^6 * x^6 → sqrt(x^12) = x^6
If it were a cube root you would be diving by 3 or using 1/3. (Although taking it out to exponent notation and then dividing by three would be a stupid way to do cube roots.)
Anonymous C replied with this 15 years ago, 6 minutes later, 46 minutes after the original post[^][v]#80,493
@previous (E)
not the answer. i meant the number under the square root. @80,485 (Triptych !!DP4/G/5A6)
sorry but i dont want to write it out on paper. good luck though
Anonymous F joined in and replied with this 15 years ago, 2 minutes later, 48 minutes after the original post[^][v]#80,494
I don't have an answer to your question yet, but the math in this problem seems weird. Maybe I am just derping, but you seem to currently be stating that 10^-4 = 10^-2. Why are you dividing the exponent by two again?
Anonymous E replied with this 15 years ago, 1 minute later, 50 minutes after the original post[^][v]#80,496
@80,493 (C) > not the answer. i meant the number under the square root.
Oh, I see why you asked OP for an example now. Yeah, the square root of a negative number would need to be expressed in terms of i.
Broseph !!fxnDb+Ve4 joined in and replied with this 15 years ago, 1 hour later, 2 hours after the original post[^][v]#80,565
Because x = x^1, and √x = x^(1/2). So, any time you divide the exponent of a number by 2, that is the same of taking the square root of that number. So, √x^6 = x^3. As an example 2^4= 16. √16= 4. 2^(4/2) = 2^2 = 4.
So when they say "divide the exponent by 2" they're really saying "take the square root of that number."
(Edited 2 minutes later.)
sim is azn joined in and replied with this 15 years ago, 8 minutes later, 2 hours after the original post[^][v]#80,576
triptych. y so math?
Triptych !!DP4/G/5A6 (OP) replied with this 15 years ago, 31 minutes later, 2 hours after the original post[^][v]#80,641
@80,565 (Broseph !!fxnDb+Ve4) @80,492 (E)
I see! Thank you very much for the explanation!
@previous (sim is azn)
So I can get to the interesting part of the textbook.