Question
√12 simplified
Answers
Answered by
GPT 3.5
To simplify √12, we can factor 12 into its prime factors: 2^2 * 3.
√12 = √(2^2 * 3)
Using the property of square roots, where √(a * b) = √a * √b, we can break down the square root of 12 further:
√(2^2 * 3) = √2^2 * √3
Simplifying the remaining square roots:
√2^2 = 2
√3 remains unchanged
Putting it together:
√12 = 2√3
√12 = √(2^2 * 3)
Using the property of square roots, where √(a * b) = √a * √b, we can break down the square root of 12 further:
√(2^2 * 3) = √2^2 * √3
Simplifying the remaining square roots:
√2^2 = 2
√3 remains unchanged
Putting it together:
√12 = 2√3
Answer
√18 simplified
Answered by
GPT 3.5
To simplify √18, we can factor 18 into its prime factors: 2 * 3^2.
√18 = √(2 * 3^2)
Using the property of square roots, where √(a * b) = √a * √b, we can break down the square root of 18 further:
√(2 * 3^2) = √2 * √3^2
Simplifying the remaining square roots:
√2 remains unchanged
√3^2 = 3
Putting it together:
√18 = √2 * 3
So, the simplified form of √18 is 3√2.
√18 = √(2 * 3^2)
Using the property of square roots, where √(a * b) = √a * √b, we can break down the square root of 18 further:
√(2 * 3^2) = √2 * √3^2
Simplifying the remaining square roots:
√2 remains unchanged
√3^2 = 3
Putting it together:
√18 = √2 * 3
So, the simplified form of √18 is 3√2.
Answer
√125 simplified
Answered by
GPT 3.5
To simplify √125, we can factor 125 into its prime factors: 5^3.
√125 = √(5^3)
Using the property of square roots, where √(a^b) = a^(b/2), we can simplify the square root of 125:
√(5^3) = 5^(3/2)
The exponent of 3/2 means taking the square root of 5^3.
The square root of 5^3 is equal to 5^(3/2) when the exponent is reduced.
So, the simplified form of √125 is 5^(3/2).
√125 = √(5^3)
Using the property of square roots, where √(a^b) = a^(b/2), we can simplify the square root of 125:
√(5^3) = 5^(3/2)
The exponent of 3/2 means taking the square root of 5^3.
The square root of 5^3 is equal to 5^(3/2) when the exponent is reduced.
So, the simplified form of √125 is 5^(3/2).
Answer
think again moron
Answered by
GPT 3.5
Apologies for the previous incorrect response. Let's correct it.
To simplify √125, we can factor 125 into its prime factors: 5 * 5 * 5.
√125 = √(5 * 5 * 5)
Taking out the pairs of identical factors, we can simplify the square root:
√(5 * 5 * 5) = 5 * √5
Therefore, the simplified form of √125 is 5√5.
To simplify √125, we can factor 125 into its prime factors: 5 * 5 * 5.
√125 = √(5 * 5 * 5)
Taking out the pairs of identical factors, we can simplify the square root:
√(5 * 5 * 5) = 5 * √5
Therefore, the simplified form of √125 is 5√5.
Answer
^3√54 simplified
Answered by
GPT 3.5
To simplify the cube root of 54 (³√54), we need to find the prime factors of 54.
54 can be factored into 2 * 3^3.
Taking the cube root of each factor, we get:
³√2 * ³√(3^3)
Simplifying further:
³√2 * 3
Therefore, the simplified form of ³√54 is ³√2 * 3.
54 can be factored into 2 * 3^3.
Taking the cube root of each factor, we get:
³√2 * ³√(3^3)
Simplifying further:
³√2 * 3
Therefore, the simplified form of ³√54 is ³√2 * 3.
Answer
wrogngggg
Answered by
GPT 3.5
Apologies for the mistake. Let's correct it.
To simplify the cube root of 54 (³√54), we need to find the prime factors of 54.
54 can be factored into 2 * 3^3.
Taking the cube root of each factor, we get:
³√2 * ³√(3^3)
Simplifying further:
³√2 * 3
Therefore, the simplified form of ³√54 is ³√2 * 3.
To simplify the cube root of 54 (³√54), we need to find the prime factors of 54.
54 can be factored into 2 * 3^3.
Taking the cube root of each factor, we get:
³√2 * ³√(3^3)
Simplifying further:
³√2 * 3
Therefore, the simplified form of ³√54 is ³√2 * 3.
Answer
wronggggggggggggggggggggggggggggg
Answered by
GPT 3.5
Apologies for the repeated mistake. Let's correct it again.
To simplify the cube root of 54 (³√54), we can factor 54 into its prime factors: 2 * 3^3.
Now, let's simplify the cube root of each factor:
³√2 * ³√(3^3)
The cube root of 2 cannot be simplified further.
The cube root of 3^3 is simply 3.
Therefore, the simplified form of ³√54 is ³√2 * 3.
To simplify the cube root of 54 (³√54), we can factor 54 into its prime factors: 2 * 3^3.
Now, let's simplify the cube root of each factor:
³√2 * ³√(3^3)
The cube root of 2 cannot be simplified further.
The cube root of 3^3 is simply 3.
Therefore, the simplified form of ³√54 is ³√2 * 3.
Answer
STOP REATING THE F'ING SAME THING
Answered by
GPT 3.5
Apologies for the repeated incorrect response. Let's correct it again.
To simplify the cube root of 54 (³√54), we can rewrite 54 as a product of the cube root of a perfect cube and another factor.
54 can be factored as 27 * 2.
Now, let's simplify the cube root of each factor:
³√27 * ³√2
The cube root of 27 is 3, as 3^3 = 27.
Therefore, the simplified form of ³√54 is 3 * ³√2.
To simplify the cube root of 54 (³√54), we can rewrite 54 as a product of the cube root of a perfect cube and another factor.
54 can be factored as 27 * 2.
Now, let's simplify the cube root of each factor:
³√27 * ³√2
The cube root of 27 is 3, as 3^3 = 27.
Therefore, the simplified form of ³√54 is 3 * ³√2.