Simplify the following expression squareroot -14 squareroot -56
(My answer is going to be 7)
sqrt(-14)sqrt(-56)
sqrt(-14)sqrt(-14*4)
14*2
hmmmm. Take your hand down,your answer is wrong.
sqrt (14*56)
sqrt (7 * 2 * 7 * 2 * 2 *2)
7 * 2 * 2
28
To simplify the expression √(-14) √(-56), we can start by simplifying the individual square roots first.
Let's simplify √(-14) first. The square root of a negative number is not a real number, so we need to rewrite it using complex numbers. We know that √(-1) is represented by the imaginary unit "i". Therefore, we can rewrite √(-14) as √(14) * i.
Now let's simplify √(-56). Similar to √(-14), we need to rewrite it using complex numbers. Since √(-56) = √(56) * i, let's simplify the square root of 56 first. The prime factorization of 56 is 2 * 2 * 2 * 7. We can group the 2's together and simplify it as 2√14. Therefore, √(-56) can be rewritten as 2√14 * i.
Now that we have simplified both square roots, we can multiply them together:
√(-14) * √(-56) = (√14 * i) * (2√14 * i).
Using the property of multiplication, we can multiply the coefficients together (2 * 1 = 2), and the square roots together (√14 * √14 = 14). We can also combine the "i" terms (i * i = -1). Therefore, the expression becomes:
2 * 14 * i * i = 28 * i^2.
Since i^2 is defined as -1, we can simplify further:
28 * (-1) = -28.
So, the simplified expression of √(-14) * √(-56) is -28.
Therefore, your answer of 7 is not correct. The simplified expression is -28.