Subtract 75–√−45–√.
To solve this problem, we need to simplify the expression step by step.
First, let's simplify the square root terms:
- √45 = √(9 * 5) = √(9) * √(5) = 3√5
Now, we can rewrite the expression:
75 - √45 - √45
Next, we can substitute the simplified square root terms:
75 - 3√5 - 3√5
Next, we can combine like terms:
75 - 6√5
Therefore, 75–√−45–√ can be simplified to 75 - 6√5.
To subtract the expression 75 – √(-45) – √(45), we need to simplify each square root separately.
Let's start with √(-45). The square root of a negative number is not a real number. It belongs to the realm of complex numbers. However, if we simplify it further, we can express it in the form of a complex number.
√(-45) = √(45 * -1) = √45 * √-1
Now, let's calculate the value of √45.
√45 = √(9 * 5) = √9 * √5 = 3√5
So, we have √(-45) = 3√5 * √-1
Since we have an √-1 term, we can represent it as 'i,' which is the imaginary unit. Therefore, √-1 = i.
Now, let's substitute √(-45) back into our original expression:
75 – √(-45) – √(45) = 75 – (3√5 * i) – (3√5)
The expression (√(-45)) equals 3√5 * i, and (√(45)) can be simplified to 3√5.
Simplifying further, we get:
75 – 3√5 * i – 3√5
Now, we can combine like terms:
75 – 3√5 * i – 3√5 = 75 – 3√5 – 3√5 * i
And that is the simplified expression for 75 – √(-45) – √(45).
To simplify the expression 75 - √(-45 - √x), we need to evaluate the square root first and then perform the subtraction.
Let's start by simplifying the expression inside the square root, -45 - √x.
Since square roots of negative numbers are not real, the expression is undefined unless x is greater than or equal to 45. Therefore, the expression -45 - √x remains as it is.
Now, we substitute -45 - √x back into the original expression:
75 - (-45 - √x)
Next, we can simplify the expression by distributing the negative sign:
75 + 45 + √x
Combine the like terms:
120 + √x
Therefore, the simplified expression is 120 + √x.