What is the square root of -72 cubed simplified
The square root of a negative number is not a real number, so the square root of -72 is not defined as a real number. Therefore, the square root of -72 cubed cannot be simplified.
To simplify the cube root of -72, we will first find the cube root of 72 and then multiply it by -1 because we are dealing with a negative number.
1. Find the cube root of 72:
∛72 ≈ 4.15888
2. Multiply the cube root by -1:
-1 * 4.15888 = -4.15888
Therefore, the simplified cube root of -72 is approximately -4.15888.
To find the square root of -72 cubed and simplify it, we'll break it down step by step:
Step 1: Start by simplifying -72 cubed.
To raise -72 to the power of 3, we multiply -72 by itself twice.
-72 × -72 × -72 = 3,110,400
Step 2: Take the square root of 3,110,400.
To find the square root, we can use a calculator or a mathematical software. Taking the square root of 3,110,400 gives us 1,764.84.
Step 3: Account for the negative sign.
Since we started with a negative number, the square root will have an imaginary component. The square root of a negative number is denoted as "i√".
So, the square root of -72 cubed simplified is written as:
i√3,110,400 = i√(2^11 × 3^2 × 5^2)
Note: The simplified form depends on the level of detail required. In this case, I expressed the answer as the product of prime factors (2, 3, and 5) for completeness. However, depending on the context, it may be sufficient to leave it as i√3,110,400.