simplfy 3*√-72
To simplify 3 * √(-72), we can first simplify the square root of -72.
The square root of -1 is expressed as "i" in mathematics, which represents the imaginary unit.
The square root of 72 can be simplified as 6√2.
Therefore, the simplified form of 3 * √(-72) is 3 * 6 * i * √2, which can be further simplified to 18i√2.
To simplify the expression 3 * √(-72), we can first look at the square root of -72. Since -72 is a negative number, we cannot simplify it directly. However, we can simplify it by factoring out a perfect square.
The square root of -1 is denoted as "i". Therefore, we can rewrite -72 as -1 * 72.
Now we have 3 * √(-1 * 72). We can further simplify the expression by splitting the square root into two parts.
3 * √(-1) * √(72)
The square root of -1 is denoted as "i", so we have:
3i * √(72)
Next, we simplify the square root of 72. We can factor out perfect square factors:
3i * √(36 * 2)
Taking the square root of 36, we get:
3i * 6 * √2
Finally, we multiply the remaining values:
18i√2
Therefore, the simplified form of 3 * √(-72) is 18i√2.
To simplify the expression 3 * √(-72), we need to simplify the square root of -72.
The square root of a negative number is not a real number, so the expression √(-72) cannot be simplified directly.
However, we can rewrite -72 as -1 * 72 and simplify it by finding the square root of 72.
The square root of 72 can be simplified as follows:
1. Find the prime factorization of 72: 72 = 2 * 2 * 2 * 3 * 3.
2. Group the prime factors in pairs: 72 = (2 * 2) * (2 * 3 * 3).
3. Rewrite the pairs as squares: 72 = 2^2 * 3^2 * 2.
4. Simplify each square: 72 = 4 * 9 * 2.
5. Multiply the simplified squares: 72 = 72.
So √72 = √(2^2 * 3^2 * 2) = 2 * 3 * √2 = 6√2.
Therefore, 3 * √(-72) = 3 * √(-1 * 72) = 3 * (6√2) = 18√2.