Find all of the real square roots of -9/16.
there are none - it is negative.
However, the real roots of 9/16 are
+3/4 and -3/4
To find the real square roots of -9/16, we need to solve the equation:
x^2 = -9/16
To begin, let's take the square root of both sides of the equation:
√(x^2) = √(-9/16)
This simplifies to:
x = ±√(-9/16)
Next, let's simplify the expression √(-9/16):
First, we simplify the fraction 9/16 by taking the square root of the numerator and denominator separately:
√9/√16 = 3/4
So now we have:
x = ±√(-1) * (3/4)
The square root of -1 is represented by the imaginary unit "i". So we can rewrite the expression as:
x = ± (3/4)i
Therefore, the real square roots of -9/16 are:
x = (3/4)i and x = -(3/4)i
To find the real square roots of a number, we need to determine the numbers that, when squared, equal the given number. In this case, we need to find the real square roots of -9/16.
To begin, let's recall that the square root of any positive number has two real roots: one positive and one negative. However, when it comes to negative numbers, there are no real square roots. The square root of a negative number is considered an imaginary number.
Now, let's focus on the given number, -9/16. Since it is negative, there are no real square roots. However, we can express the square root in terms of an imaginary number.
When we simplify the square root of -9/16, we get:
√(-9/16) = √(-9)/√(16)
Since √(-9) is not a real number, it is often expressed as √(-1) * √(9), which simplifies to i * 3.
Therefore, the real square roots of -9/16 are ±(3/4)i, where i represents the imaginary unit.