Evaluate the expression √−7/√ −6√−5 and write the result in the form a+bi.
I keep getting b as 0.483i but apparently its wrong?
Well, you need to work on using parentheses
√−7/√−6√−5 means (√−7/√−6)(√−5)
= 7i/6i * 5i
= 35i^2/6i
= 35/6 i = 5.83i
√−7/(√−6√−5) = 7i/-30 = -0.233i
0.483 = 29/60
Too bad you didn't bother to show your work, eh?
Or is there a typo in the problem?
Tried that answer as well but the website is till telling me its wrong. Could be a typo will have to check with the instructor.
To evaluate the expression √(-7) / √(-6√(-5)), we need to simplify each square root separately before performing the division.
First, let's simplify √(-7). Since the square root of a negative number is not a real number, we need to rewrite it using imaginary numbers. The square root of -1 is denoted as "i", so we can write √(-7) as √(7) * i.
Next, let's simplify √(-5). Similarly, we can rewrite it as √(5) * i.
Now, we have √(7) * i / √(6 * √(5)).
To simplify the denominator, we can multiply the square roots together:
√(6 * √(5)) = √6 * √(√5) = √6 * √(5^(1/2)) = √6 * (5^(1/4)).
Now we have √(7) * i / (√6 * (5^(1/4))).
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is (√6 * (5^(1/4))):
(√(7) * i / (√6 * (5^(1/4)))) * (√6 * (5^(1/4))) / (√6 * (5^(1/4)))
This simplifies to (√(7) * i * √6 * (5^(1/4))) / (√6 * (5^(1/4)) * √6 * (5^(1/4))).
Canceling out the terms that are the same in the numerator and denominator, we are left with:
(√(7) * i) / 6.
So, the simplified expression is (√(7) * i) / 6.
Therefore, the result in the form of a+bi is 0 + (√(7) / 6)i.
To evaluate the expression √−7/√−6√−5 in the form a+bi, we first need to simplify the expression and then rationalize the denominator. Let's break down the steps:
Step 1: Simplify the expression
√−7/√−6√−5 can be simplified as follows:
√(−7)/√(−6)√(−5)
Step 2: Rationalize the denominator
Rationalize the denominator by multiplying both the numerator and denominator by √(−6)√(−5):
√(−7)/√(−6)√(−5) × (√(−6)√(−5))/(√(−6)√(−5))
This simplifies to:
√(−7)√(−6)√(−5)/√(−6)√(−6)√(−5)
Step 3: Simplify further
Now, we can simplify the expression by canceling out the common factors:
√(−7)√(−6)√(−5)/√(−6)√(−6)√(−5)
This simplifies to:
(√(−7))/√(−6)
Step 4: Rationalize the denominator again
To rationalize the denominator, we need to multiply the numerator and denominator by the conjugate of the denominator:
(√(−7))/√(−6) × (√(−6))/((√(−6))(√(−6)))
This simplifies to:
(√(−7)√(−6))/(√(−6)∙√(−6)∙√(−6))
Step 5: Simplify further
We have:
(√(−7)√(−6))/(√(−6)∙√(−6)∙√(−6))
Using the property of square roots that √(ab) = √a√b, we can simplify it as:
(√(−7)√(−6))/(−6∙√(−6))
Step 6: Final simplification
We can further simplify it as:
(√42∙i)/(−6∙i√6)
Since i^2 = -1, we can simplify it as:
(-√42)/(6√6)
Therefore, the final result in the form a+bi is:
(-√42)/(6√6)