Question
Question: How do you simplify \(\sqrt{-1256}\)?...
How do you simplify −1256?
Solution
In the above question, we have been given a square root expression to be simplified. To simplify it, we need to use the law of radicals which is given by ab=ab so that the given expression reduces to −11256. Then, since i=−1, the given expression will become 1256i. Then we need to simplify the expression 1256 by writing the prime factorisation of the number 1256. From the prime factorisation, we can take out the highest perfect square from the square root to get the final simplified expression.
Complete step-by-step answer:
The expression given in the above question is
⇒−1256
Now, using the law of radicals given by ab=ab, we can write the above expression as
⇒−11256
Now, we know that −1 is a complex number which is equal to i so that we can put −1=1 in the above expression to get
⇒1256i.......(i)
Now, in order to further simplify the above 0065pression, we have to write the prime factorization for the number 1256, as shown below.