To simplify 12−−√, we first simplify the expression underneath the radical:
√12 can be simplified further by finding the largest perfect square that divides evenly into 12. The largest perfect square is 4 because 4 * 3 = 12.
Therefore, √12 = √(4 * 3) = √(4) * √(3) = 2√3.
So, 12−−√ simplified is 2√3.
What is 12−−√ simplified?(1 point)
25 answers
What is 18−−√ simplified?(1 point)
To simplify 18−−√, we first simplify the expression underneath the radical:
√18 can be simplified further by finding the largest perfect square that divides evenly into 18. The largest perfect square is 9 because 9 * 2 = 18.
Therefore, √18 = √(9 * 2) = √(9) * √(2) = 3√2.
So, 18−−√ simplified is 3√2.
√18 can be simplified further by finding the largest perfect square that divides evenly into 18. The largest perfect square is 9 because 9 * 2 = 18.
Therefore, √18 = √(9 * 2) = √(9) * √(2) = 3√2.
So, 18−−√ simplified is 3√2.
What is 125−−−√ simplified?(1 point)
To simplify 125−−−√, we need to find the square root of 125:
√125 can be simplified by recognizing that 125 can be expressed as the square of a smaller number. The largest perfect cube that divides evenly into 125 is 5, because 5 * 5 * 5 = 125.
Therefore, √125 = √(5^3) = √(5^2 * 5) = 5√5.
So, 125−−−√ simplified is 5√5.
√125 can be simplified by recognizing that 125 can be expressed as the square of a smaller number. The largest perfect cube that divides evenly into 125 is 5, because 5 * 5 * 5 = 125.
Therefore, √125 = √(5^3) = √(5^2 * 5) = 5√5.
So, 125−−−√ simplified is 5√5.
What is 54−−√3 simplified?
To simplify 54−−√3, we first simplify the expression underneath the radical:
√3 cannot be simplified any further because 3 is a prime number.
Therefore, 54−−√3 remains as 54−√3.
√3 cannot be simplified any further because 3 is a prime number.
Therefore, 54−−√3 remains as 54−√3.
wrong
Apologies for the incorrect response. Let's correct it.
To simplify √54/3, we can simplify the expression inside the square root:
√54 can be simplified by finding the largest perfect square that divides evenly into 54. The largest perfect square is 9 because 9 * 6 = 54.
Therefore, √54 = √(9 * 6) = √(9) * √(6) = 3√6.
So, √54/3 simplified is √6.
To simplify √54/3, we can simplify the expression inside the square root:
√54 can be simplified by finding the largest perfect square that divides evenly into 54. The largest perfect square is 9 because 9 * 6 = 54.
Therefore, √54 = √(9 * 6) = √(9) * √(6) = 3√6.
So, √54/3 simplified is √6.
that is wrong
Apologies for the confusion. Let's correct it.
To simplify √54/3, we can simplify the expression inside the square root:
√54 can be simplified further by finding the largest perfect square that divides evenly into 54. The largest perfect square is 36 because 36 * 1.5 = 54.
Therefore, √54 = √(36 * 1.5) = √(36) * √(1.5) = 6√1.5.
So, √54/3 simplified is 2√1.5.
To simplify √54/3, we can simplify the expression inside the square root:
√54 can be simplified further by finding the largest perfect square that divides evenly into 54. The largest perfect square is 36 because 36 * 1.5 = 54.
Therefore, √54 = √(36 * 1.5) = √(36) * √(1.5) = 6√1.5.
So, √54/3 simplified is 2√1.5.
What is −72−−−−√3 simplified?
To simplify −72−−−−√3, we first simplify the expression inside the radical:
√3 cannot be simplified any further because 3 is a prime number.
Therefore, −72−−−−√3 remains as −72−√3.
√3 cannot be simplified any further because 3 is a prime number.
Therefore, −72−−−−√3 remains as −72−√3.
What is 3√−72 simplified?
To simplify 3√(-72), we need to simplify the expression inside the radical:
√(-72) can be simplified by factoring out a -1 from -72:
√(-72) = √(-1 * 72) = √(-1) * √(72) = i√72.
Now, let's simplify √72:
√72 can be simplified further by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √72 = √(36 * 2) = √(36) * √(2) = 6√2.
Finally, substituting the simplified value back into the original expression:
3√(-72) = 3(i√72) = 3(i)(6√2) = 18i√2.
So, 3√(-72) simplified is 18i√2.
√(-72) can be simplified by factoring out a -1 from -72:
√(-72) = √(-1 * 72) = √(-1) * √(72) = i√72.
Now, let's simplify √72:
√72 can be simplified further by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √72 = √(36 * 2) = √(36) * √(2) = 6√2.
Finally, substituting the simplified value back into the original expression:
3√(-72) = 3(i√72) = 3(i)(6√2) = 18i√2.
So, 3√(-72) simplified is 18i√2.
that is wrong!
Apologies for the incorrect response. Let's correct it.
To simplify 3√(-72), we need to simplify the expression inside the radical:
Since -72 is a negative number, the square root of -72 is not a real number. It is an imaginary number.
The square root of -1 is denoted as "i", which is an imaginary unit. So, we can rewrite 3√(-72) as 3√(72)√(-1).
Now, let's simplify the square root of 72:
√(72) = √(36 * 2) = 6√2.
Therefore, 3√(-72) = 3(6√2)i = 18√2i.
So, the simplified form of 3√(-72) is 18√2i.
To simplify 3√(-72), we need to simplify the expression inside the radical:
Since -72 is a negative number, the square root of -72 is not a real number. It is an imaginary number.
The square root of -1 is denoted as "i", which is an imaginary unit. So, we can rewrite 3√(-72) as 3√(72)√(-1).
Now, let's simplify the square root of 72:
√(72) = √(36 * 2) = 6√2.
Therefore, 3√(-72) = 3(6√2)i = 18√2i.
So, the simplified form of 3√(-72) is 18√2i.
thats incorrect
Apologies for the previous incorrect response. Let's correct it.
To simplify 3√(-72), we first note that the square root of a negative number is not defined in the real number system. However, if we consider the complex number system, which includes imaginary numbers, we can simplify the expression.
We can rewrite -72 as -1 * 72.
Now, let's simplify the expression inside the radical:
√(-1 * 72) = √(-1) * √(72) = i * √(72).
Next, let's simplify √(72):
√(72) can be simplified by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √(72) = √(36 * 2) = √(36) * √(2) = 6√2.
Finally, substituting the simplified values back into the original expression:
3√(-72) = 3(i * 6√2) = 18i√2.
So, the simplified form of 3√(-72) is 18i√2.
To simplify 3√(-72), we first note that the square root of a negative number is not defined in the real number system. However, if we consider the complex number system, which includes imaginary numbers, we can simplify the expression.
We can rewrite -72 as -1 * 72.
Now, let's simplify the expression inside the radical:
√(-1 * 72) = √(-1) * √(72) = i * √(72).
Next, let's simplify √(72):
√(72) can be simplified by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √(72) = √(36 * 2) = √(36) * √(2) = 6√2.
Finally, substituting the simplified values back into the original expression:
3√(-72) = 3(i * 6√2) = 18i√2.
So, the simplified form of 3√(-72) is 18i√2.
thats is wrong you are not doing it correct!!
Apologies for the confusion. Let's correct the response and simplify 3√(-72) properly.
To simplify 3√(-72), we need to rationalize the denominator to remove the radical from the denominator.
First, let's simplify the expression inside the radical:
√(-72) can be written as √(72)√(-1).
Now, let's simplify √(72):
√(72) can be simplified by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √(72) = √(36 * 2) = √(36) * √(2) = 6√(2).
Substituting back into the expression:
3√(-72) = 3(6√(2))√(-1) = 18√(2)√(-1) = 18√(2i)
So, the simplified form of 3√(-72) is 18√(2i).
To simplify 3√(-72), we need to rationalize the denominator to remove the radical from the denominator.
First, let's simplify the expression inside the radical:
√(-72) can be written as √(72)√(-1).
Now, let's simplify √(72):
√(72) can be simplified by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √(72) = √(36 * 2) = √(36) * √(2) = 6√(2).
Substituting back into the expression:
3√(-72) = 3(6√(2))√(-1) = 18√(2)√(-1) = 18√(2i)
So, the simplified form of 3√(-72) is 18√(2i).
What is 3√−72 simplified?
Apologies for the confusion in previous responses. Let's simplify 3√(-72) properly.
To simplify 3√(-72), we need to break it down into a real and imaginary part.
We can write -72 as -1 * 72.
√(-72) can be rewritten as √(72) * √(-1).
Let's simplify √(72):
√(72) can be simplified by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √(72) = √(36 * 2) = √(36) * √(2) = 6√2.
Now, let's simplify √(-1):
√(-1) is equal to the imaginary unit "i".
Finally, substituting the simplified values back into the original expression:
3√(-72) = 3(6√2)i = 18√2i.
So, the simplified form of 3√(-72) is 18√2i.
To simplify 3√(-72), we need to break it down into a real and imaginary part.
We can write -72 as -1 * 72.
√(-72) can be rewritten as √(72) * √(-1).
Let's simplify √(72):
√(72) can be simplified by factoring out perfect squares. The largest perfect square that divides evenly into 72 is 36 because 36 * 2 = 72.
Therefore, √(72) = √(36 * 2) = √(36) * √(2) = 6√2.
Now, let's simplify √(-1):
√(-1) is equal to the imaginary unit "i".
Finally, substituting the simplified values back into the original expression:
3√(-72) = 3(6√2)i = 18√2i.
So, the simplified form of 3√(-72) is 18√2i.
Answers since the bot is being dumb
1. 2√3
2. 3√2
3. 5√5
4. 3 ^3√2 (2 is normal)
5. -2 ^ 3 √9 (9 is normal)
1. 2√3
2. 3√2
3. 5√5
4. 3 ^3√2 (2 is normal)
5. -2 ^ 3 √9 (9 is normal)
My apologies if there was any confusion earlier. Let's go through each question and provide the correct simplified forms:
1. 12−−√ simplified = 2√3
2. 18−−√3 simplified = 3√2
3. 125−−−√ simplified = 5√5
4. 3√−72 simplified = -2√3
5. −72−−−−√3 simplified = -2√9
Please let me know if there is anything else I can assist you with!
1. 12−−√ simplified = 2√3
2. 18−−√3 simplified = 3√2
3. 125−−−√ simplified = 5√5
4. 3√−72 simplified = -2√3
5. −72−−−−√3 simplified = -2√9
Please let me know if there is anything else I can assist you with!