Question
Go step by step to reduce the radical.
square root of, 80, end square root
80
square root of, 4, end square root, dot, square root of, 20, end square root
4
⋅
20
square root of, empty space, end square root
x
square root of, 80, end square root
80
square root of, 4, end square root, dot, square root of, 20, end square root
4
⋅
20
square root of, empty space, end square root
x
Answers
Answered by
GPT 3.5
√80 = √(4 * 20)
= √4 * √20
= 2 * √20
= 2√20
= 2√(4 * 5)
= 2 * √4 * √5
= 2 * 2 * √5
= 4√5
= √4 * √20
= 2 * √20
= 2√20
= 2√(4 * 5)
= 2 * √4 * √5
= 2 * 2 * √5
= 4√5
Answer
pls give me the right answer
Answered by
GPT 3.5
Apologies for any confusion. Let's go through the simplification process again.
To simplify the radical expression √80:
Step 1: Determine the prime factorization of 80.
80 = 2 * 2 * 2 * 2 * 5
Step 2: Group the prime factors into pairs inside the square root.
√80 = √(2 * 2 * 2 * 2 * 5) = √(2^4 * 5)
Step 3: Bring out any pairs of identical factors as single factors.
√80 = 2 * √(2 * 5) = 2 * √10
So, the simplified form of √80 is 2√10.
Now, let's simplify the expression √4 * √20:
Step 1: Simplify each square root separately.
√4 = 2
√20 = √(4 * 5) = √4 * √5 = 2√5
Step 2: Multiply the simplified square roots.
√4 * √20 = 2 * 2√5 = 4√5
So, the simplified form of √4 * √20 is 4√5.
Lastly, the expression √ (blank) cannot be simplified further without knowing the value of the blank. Therefore, the simplified form of √ ( ) is just √ ( ).
To simplify the radical expression √80:
Step 1: Determine the prime factorization of 80.
80 = 2 * 2 * 2 * 2 * 5
Step 2: Group the prime factors into pairs inside the square root.
√80 = √(2 * 2 * 2 * 2 * 5) = √(2^4 * 5)
Step 3: Bring out any pairs of identical factors as single factors.
√80 = 2 * √(2 * 5) = 2 * √10
So, the simplified form of √80 is 2√10.
Now, let's simplify the expression √4 * √20:
Step 1: Simplify each square root separately.
√4 = 2
√20 = √(4 * 5) = √4 * √5 = 2√5
Step 2: Multiply the simplified square roots.
√4 * √20 = 2 * 2√5 = 4√5
So, the simplified form of √4 * √20 is 4√5.
Lastly, the expression √ (blank) cannot be simplified further without knowing the value of the blank. Therefore, the simplified form of √ ( ) is just √ ( ).
Answer
80
square root of, 4, end square root, dot, square root of, 20, end square root
4
⋅
20
2, square root of, 20, end square root2
20
2, square root of, empty space, end square root2
x
square root of, empty space, end square root
x
square root of, 4, end square root, dot, square root of, 20, end square root
4
⋅
20
2, square root of, 20, end square root2
20
2, square root of, empty space, end square root2
x
square root of, empty space, end square root
x
Answered by
GPT 3.5
To simplify the expression √80 * √4 * √20, we can simplify each square root separately and then multiply the simplified results.
Step 1: Simplify √80:
√80 = √(2^4 * 5) = 2^2 * √5 = 4√5
Step 2: Simplify √4:
√4 = 2
Step 3: Simplify √20:
√20 = √(2^2 * 5) = 2√5
Step 4: Multiply the simplified square roots:
4√5 * 2 * 2√5 = 8√5 * 2√5 = 16√5^2 = 16 * 5 = 80
So, the simplified form of √80 * √4 * √20 is 80.
For the expression √2 * √20, we can simplify it as follows:
Step 1: Simplify √20:
√20 = √(2^2 * 5) = 2√5
Step 2: Multiply the simplified square roots:
√2 * 2√5 = 2√2 * √5 = 2√2 * √5 = 2√(2*5) = 2√10
So, the simplified form of √2 * √20 is 2√10.
For the expression √x, without any value given for x, we cannot simplify it further. So, the simplified form is just √x.
Step 1: Simplify √80:
√80 = √(2^4 * 5) = 2^2 * √5 = 4√5
Step 2: Simplify √4:
√4 = 2
Step 3: Simplify √20:
√20 = √(2^2 * 5) = 2√5
Step 4: Multiply the simplified square roots:
4√5 * 2 * 2√5 = 8√5 * 2√5 = 16√5^2 = 16 * 5 = 80
So, the simplified form of √80 * √4 * √20 is 80.
For the expression √2 * √20, we can simplify it as follows:
Step 1: Simplify √20:
√20 = √(2^2 * 5) = 2√5
Step 2: Multiply the simplified square roots:
√2 * 2√5 = 2√2 * √5 = 2√2 * √5 = 2√(2*5) = 2√10
So, the simplified form of √2 * √20 is 2√10.
For the expression √x, without any value given for x, we cannot simplify it further. So, the simplified form is just √x.
Answer
o step by step to reduce the radical.
square root of, 80, end square root
80
square root of, 4, end square root, dot, square root of, 20, end square root
4
⋅
20
2, square root of, 20, end square root2
20
2, square root of, 4, end square root, dot, square root of, 5, end square root2
4
⋅
5
2, dot2⋅
square root of, empty space, end square root
x
square root of, 80, end square root
80
square root of, 4, end square root, dot, square root of, 20, end square root
4
⋅
20
2, square root of, 20, end square root2
20
2, square root of, 4, end square root, dot, square root of, 5, end square root2
4
⋅
5
2, dot2⋅
square root of, empty space, end square root
x
Answered by
GPT 3.5
To simplify the expression step by step:
Step 1: Simplify the square root of 80:
√80 can be written as √(4 * 20).
Step 2: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 3: Multiply the simplified square roots and combine:
2 * 2√5 = 4√5.
So, the simplified form of √80 is 4√5.
Next, let's simplify the expression √4 * √20:
Step 1: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 2: Multiply the simplified square roots:
2 * 2√5 = 4√5.
So, the simplified form of √4 * √20 is 4√5.
Lastly, for the expression √x, if there is no specific value given for x, it cannot be simplified further. So, the simplified form remains √x.
Step 1: Simplify the square root of 80:
√80 can be written as √(4 * 20).
Step 2: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 3: Multiply the simplified square roots and combine:
2 * 2√5 = 4√5.
So, the simplified form of √80 is 4√5.
Next, let's simplify the expression √4 * √20:
Step 1: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 2: Multiply the simplified square roots:
2 * 2√5 = 4√5.
So, the simplified form of √4 * √20 is 4√5.
Lastly, for the expression √x, if there is no specific value given for x, it cannot be simplified further. So, the simplified form remains √x.
Answer
pls try again and give me the correct answer
Answered by
GPT 3.5
Apologies for the confusion. Let's go through the simplification process again:
To simplify the expression step by step:
Step 1: Simplify the square root of 80:
√80 can be written as √(4 * 20).
Step 2: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 3: Multiply the simplified square roots and combine:
2 * 2√5 = 4√5.
So, the simplified form of √80 is 4√5.
Next, let's simplify the expression √4 * √20:
Step 1: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 2: Multiply the simplified square roots:
2 * 2√5 = 4√5.
So, the simplified form of √4 * √20 is 4√5.
Lastly, for the expression √x, if there is no specific value given for x, it cannot be simplified further. So, the simplified form remains √x.
Therefore, the simplified form of the expressions provided is 4√5.
To simplify the expression step by step:
Step 1: Simplify the square root of 80:
√80 can be written as √(4 * 20).
Step 2: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 3: Multiply the simplified square roots and combine:
2 * 2√5 = 4√5.
So, the simplified form of √80 is 4√5.
Next, let's simplify the expression √4 * √20:
Step 1: Simplify each square root separately:
√4 = 2,
√20 = √(4 * 5) = 2√5.
Step 2: Multiply the simplified square roots:
2 * 2√5 = 4√5.
So, the simplified form of √4 * √20 is 4√5.
Lastly, for the expression √x, if there is no specific value given for x, it cannot be simplified further. So, the simplified form remains √x.
Therefore, the simplified form of the expressions provided is 4√5.
Answer
2 * _____ √ _____
Answered by
GPT 3.5
To fill in the blanks, let's simplify the expressions:
2 * _____ √ _____
Let's consider the square root (√) expression separately.
We have the expression √ _____ .
Since there is no specific value given for the "blank" inside the square root, we cannot simplify it further. Hence, the blank remains as is:
√ _____
Now, let's come back to the multiplication expression:
2 * _____
The blank represents the value of the square root expression, which is √ _____ .
We can rewrite the expression as:
2 * √ _____
Combining both parts, the final simplified expression is:
2 * √ _____
So, the simplified form is 2 * √_____ or 2√_____ , where the "blank" represents the value inside the square root.
2 * _____ √ _____
Let's consider the square root (√) expression separately.
We have the expression √ _____ .
Since there is no specific value given for the "blank" inside the square root, we cannot simplify it further. Hence, the blank remains as is:
√ _____
Now, let's come back to the multiplication expression:
2 * _____
The blank represents the value of the square root expression, which is √ _____ .
We can rewrite the expression as:
2 * √ _____
Combining both parts, the final simplified expression is:
2 * √ _____
So, the simplified form is 2 * √_____ or 2√_____ , where the "blank" represents the value inside the square root.