Bot, what is -72√3 simplified
-72√3 cannot be further simplified because √3 is an irrational number.
Bot, What Is 3√54 simplified
To simplify 3√54, we can break it down further. We know that the square root of 54 can be simplified as the square root of 9 times the square root of 6. The square root of 9 is 3. Therefore, we have 3 times the square root of 6. Thus, 3√54 simplified is 3√6.
Bot, it's incorrect
Apologies for the error. Let me correct it.
To simplify 3√54, we can start by finding the factors of 54.
54 can be written as 2 x 27, and further as 2 x 3 x 9.
Now, 9 is a perfect square, so we can simplify the square root of 9 to 3.
Therefore, 3√54 simplified is 3 x √2 x 3, which simplifies to 9√2.
Still incorrect
Apologies once again for the mistake. Let's correct it.
To simplify 3√54, we can begin by identifying the perfect square factors of 54. We find that 54 can be expressed as 9 times 6.
Now, the square root of 9 is 3, and √6 cannot be simplified further since 6 does not have any perfect square factors.
Therefore, 3√54 simplified is 3√6.
It's not 3√6
Apologies for the previous incorrect response. Let's simplify 3√54 correctly.
To simplify 3√54, we can start by finding the factors of 54.
54 can be written as 2 x 27, and further as 2 x 3 x 9.
Now, 9 is a perfect square, so we can simplify the square root of 9 to 3.
Therefore, 3√54 simplified is 3√(2 x 3) which equals 3√6.
Bot what is 3√-72 simplified
To simplify 3√(-72), we can start by factoring out the perfect square from -72. We find that -72 can be written as -1 x 36 x 2.
Next, we can simplify the square root of 36, which is 6. However, since we have a negative sign in front, we need to consider the imaginary unit, "i". The square root of -1 is defined as "i". Therefore, the simplified form of 3√(-72) is 6i√2.
Bot it's wrong
Apologies for the incorrect response. Let's correct it.
To simplify 3√(-72), we can start by factoring out the perfect square from -72. We find that -72 can be written as -1 x 36 x 2.
Next, we can simplify the square root of 36, which is 6. However, in the case of taking the cube root of a negative number, we need to consider complex numbers.
When simplifying the cube root of a negative number, we can rewrite it as the cube root of the absolute value of the number times -1.
So, 3√(-72) can be written as 3√(72) x -1.
Now, we can simplify the cube root of 72. The largest perfect cube that divides 72 is 8. We can rewrite 72 as 8 x 9.
Therefore, 3√(-72) simplifies to 3(-2)√2, which equals -6√2.
Still wrong
Apologies once again for the mistake. Let's correct it.
To simplify 3√(-72), we start by noting that the cube root of a negative number is possible.
Now, let's factor out the perfect cube from -72. We find that -72 can be written as -1 x 36 x 2.
The cube root of -1 is -1, and the cube root of 36 is 6. Therefore, 3√(-72) simplifies to -6√2.
Bot, can you simplify 3√54 and 3√-72
Certainly! Let's simplify both expressions:
1. 3√54:
To simplify 3√54, we can factorize 54 into 2 × 3^3. Since 3 is a perfect cube, we can take it out of the cube root. The simplified form of 3√54 is 3 × 3√2, which simplifies to 9√2.
2. 3√(-72):
Here, we can factorize -72 into -1 × 2^3 × 3^2. Similar to the previous case, we can take out -1 and 3 as perfect cubes from the cube root. Therefore, the simplified form of 3√(-72) is 3 × -2 × √2, which simplifies to -6√2.
To summarize:
- 3√54 simplifies to 9√2.
- 3√(-72) simplifies to -6√2.
It's wrong
Apologies for the confusion. Let's correct it.
1. To simplify 3√54, we can factorize 54 into 2 x 3^3. The cube root of 3^3 is 3. Therefore, 3√54 simplifies to 3 x 3√2, which is equal to 9√2.
2. For 3√(-72), we can factorize -72 into -1 x 2^3 x 3^2. Now, let's simplify the cube root. The cube root of -1 is -1, and the cube root of 2^3 x 3^2 is 2√3.
So, 3√(-72) simplifies to -1 x 2√3, which equals -2√3.
To summarize:
- 3√54 simplifies to 9√2.
- 3√(-72) simplifies to -2√3.