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
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
√80 = √(4 * 20)
= √4 * √20
= 2 * √20
So, the square root of 80 is 2√20.
Next, let's simplify √20:
√20 = √(4 * 5)
= √4 * √5
= 2 * √5
Therefore, 2√20 becomes 2 * 2 * √5, which is equal to 4√5.
Finally, we have reduced the radical √80 to 4√5.
To reduce the radical √80, we can start by splitting the number into its prime factors: 80 = 2 x 2 x 2 x 2 x 5.
Next, we can group the factors into pairs where there are two of the same factor. In this case, we have two pairs of 2s: (2 x 2) x (2 x 2) x 5.
Since each pair of 2s can be simplified to just one 2, we can rewrite the expression as: 2 x 2 x 5 = 20.
Therefore, the simplified form of √80 is 2√5.
Moving on to the expression √4 * √20.
First, let's simplify the square root of 4, which is 2. Now we have 2 * √20.
Next, let's factorize 20 into its prime factors: 20 = 2 x 2 x 5.
We can simplify this expression as 2 * 2√5 = 4√5.
Therefore, the simplified form of √4 * √20 is 4√5.
Finally, we have the expression 2√20 * √4.
Let's start by simplifying the square root of 20. We already know that √20 is equal to 2√5.
Now we can rewrite the expression as 2√5 * √4.
Since the square root of 4 is 2, we can further simplify the expression as 2 * 2√5 = 4√5.
Therefore, the simplified form of 2√20 * √4 is 4√5.
thank you now we have one more problem like this
Sure, I'm happy to help. Please provide the problem you would like assistance with.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, empty space, end square root
x
square root of, empty space, end square root
x
To simplify the square root of 80, we can first factor out any perfect square factors from within the square root. In this case, 80 can be factored as the product of 4 and 20.
√80 = √(4 * 20)
Next, we can take the square root of each perfect square factor and remove it from the square root:
√(4 * 20) = √4 * √20
The square root of 4 is 2, so we can simplify further:
2 * √20
Next, we look for any perfect square factors within the remaining radicand, which is 20 in this case. The perfect square factor of 20 is 4.
2 * √(4 * 5)
We can simplify further by taking the square root of 4:
2 * 2 * √5
Finally, multiplying the numbers outside the square root:
4√5
So, the simplified form of the square root of 80 is 4√5.
To reduce the radical √224, we can start by factoring the number into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, we can group the factors into pairs where there are two of the same factor. In this case, we have four pairs of 2s: (2 x 2) x (2 x 2) x 7.
Since each pair of 2s can be simplified to just one 2, we can rewrite the expression as: 2 x 2 x 2 x 7 = 56.
Therefore, the simplified form of √224 is 2√56.
Next, let's simplify √56.
Similar to before, let's factorize 56 into its prime factors: 56 = 2 x 2 x 2 x 7.
Just like how we simplified √224, we can simplify √56 by grouping the factors into pairs of the same number.
We have two pairs of 2s: (2 x 2) x 2 x 7.
Since each pair of 2s can be simplified to just one 2, we can rewrite the expression as: 2 x 2 x 2 x 7 = 8√7.
Therefore, the simplified form of √56 is 8√7.
Finally, we have reduced the radical √224 to 2√56, and further simplified to 8√7.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
square root of, empty space, end square root
x
To simplify the square root of 224, we can start by factoring the number into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, we can split the radical into separate square roots: √224 = √(4 x 56).
We can simplify each square root separately:
√4 = 2
√56 = √(4 x 14).
Now we have 2√(4 x 14).
We can simplify the square root of 4 as √4 = 2.
So, we have 2 x 2√14.
Multiplying the numbers outside the square root, we get 4√14.
Therefore, the simplified form of √224 is 4√14.
Can u try again
Apologies for any confusion. Let's try simplifying the square root of 224 once more.
To simplify √224, we can start by factoring out any perfect square factors from within the square root. In this case, 224 can be factored as the product of 16 and 14.
√224 = √(16 * 14)
Next, we can take the square root of each perfect square factor and remove it from the square root:
√(16 * 14) = √16 * √14
The square root of 16 is 4, and the square root of 14 cannot be simplified further:
4 * √14
Therefore, the simplified form of √224 is 4√14.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
4
square root of, empty space, end square root
x
To simplify the square root of 224, we can break it down into the square root of its factors.
First, let's factorize 224 into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, let's split the square root: √224 = √(4 x 56).
We can simplify each square root separately:
√4 = 2.
Now we have: 2√56.
Next, let's simplify √56.
We can factorize 56 into its prime factors: 56 = 2 x 2 x 2 x 7.
We can split the square root: 2√(2 x 2 x 7).
The square root of 2 is √2.
Putting it all together, we have: 2√(2 x 2 x 7) = 2 x 2 x √7 = 4√7.
Therefore, the simplified form of √224 is 4√7.
Take the square root of the perfect square: square root of, 4, end square root
4
Leave square root of, 56, end square root
56
inside the radical for now.
To simplify the square root of 224, let's start by taking the square root of the perfect square factor, which is 4:
√4 = 2.
Now we can write the simplified form as:
2√56.
The square root of 56 cannot be simplified further since there are no perfect square factors in it. Thus, the final simplified form of √224 is:
2√56.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
2, square root of, 56, end square root2
56
2, square root of, empty space, end square root2
x
square root of, empty space, end square root
x
To reduce the radical √224, we can start by factoring the number into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, we can split the radical into separate square roots: √224 = √(4 x 56).
We can simplify each square root separately:
√4 = 2
√56 remains as it is.
Now we have 2√56.
Therefore, the simplified form of √224 is 2√56.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
2, square root of, 56, end square root2
56
2, square root of, 4, end square root, dot, square root of, 14, end square root2
4
⋅
14
2, dot2⋅
square root of, empty space, end square root
x
To simplify the square root of 224, we can start by factoring the number into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, we can split the radical into separate square roots: √224 = √(4 x 56).
We can simplify each square root separately:
√4 = 2
√56 = √(4 x 14).
Now we have 2√(4 x 14).
We can simplify the square root of 4 as √4 = 2.
So, we have 2 x 2√14.
Multiplying the numbers outside the square root, we get 4√14.
Therefore, the simplified form of √224 is 4√14.
whats next
If you would like to continue simplifying the expression, we can further look for any perfect square factors within the remaining √14.
Since 14 does not have any perfect square factors other than 1, we cannot simplify it further.
Therefore, the simplified form of √224 or √(4 x 56) is 4√14.
If you have any other questions or mathematical expressions you would like to simplify, feel free to let me know!
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
2, square root of, 56, end square root2
56
2, square root of, 4, end square root, dot, square root of, 14, end square root2
4
⋅
14
2, dot2⋅
4
square root of, empty space, end square root
x
To reduce the radical √224, we can start by factoring the number into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, we can split the radical into separate square roots: √224 = √(4 x 56).
We can simplify each square root separately:
√4 = 2
√56 remains as it is.
Now we have 2√56.
Therefore, the simplified form of √224 or √(4 x 56) is 2√56.
If you would like to simplify further, we can continue.
Next, let's simplify √56.
We can factorize 56 into its prime factors: 56 = 2 x 2 x 2 x 7.
We can split the square root: 2√(2 x 2 x 7).
Simplifying each factor separately:
√2 = √2
√2 x √2 = 2 x 2 = 4
√7 remains as it is.
Putting it all together, we have: 2 x 4√7 = 8√7.
Therefore, the final simplified form of √224 or √(4 x 56) is 8√7.
Take the square root of the perfect square: square root of, 4, end square root
4
Leave square root of, 14, end square root
14
inside the radical for now.
To simplify the square root of 224, we can start by taking the square root of the perfect square factor, which is 4:
√4 = 2.
Now we can write the simplified form as:
2√14.
The square root of 14 cannot be simplified further since there are no perfect square factors in it. Thus, the final simplified form of √224 is:
2√14.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
2, square root of, 56, end square root2
56
2, square root of, 4, end square root, dot, square root of, 14, end square root2
4
⋅
14
2, dot, 2, square root of, 14, end square root2⋅2
14
square root of, empty space, end square root
x
Apologies for the error in the previous response. Let's simplify the square root of 224 correctly:
To simplify √224, we can start by factoring the number into its prime factors: 224 = 2 x 2 x 2 x 2 x 7.
Next, we can split the radical into separate square roots: √224 = √(4 x 56).
We can simplify each square root separately:
√4 = 2.
√56 remains as it is.
Now we have 2√56.
Therefore, the simplified form of √224 or √(4 x 56) is 2√56.
If you would like to simplify further, we can continue.
Next, let's simplify √56.
We can factorize 56 into its prime factors: 56 = 2 x 2 x 2 x 7.
We can split the square root: 2√(2 x 2 x 7).
Simplifying each factor separately:
√2 = √2.
√2 x √2 = 2.
Putting it all together, we have: 2 x 2√7 = 4√7.
Therefore, the final simplified form of √224 or √(4 x 56) is 4√7.
Multiply the two numbers in front of the radical.
Keep the inside of the radical the same.
I apologize for the confusion in my previous responses. Let's simplify the square root of 224 correctly.
To simplify √224, we can multiply the two numbers outside the radical and keep the inside of the radical the same.
The square root of 4 is 2, and the square root of 56 remains as √56.
So, the simplified form of √224 is simply 2√56.
Again, I apologize for the confusion in earlier responses. Thank you for your patience.
Pls give me the right answer
I apologize for the confusion. Let's go through the simplification process again:
√224 can be written as √(4 * 56).
The square root of 4 is 2, so we have 2√(56).
Therefore, the simplified form of √224 is 2√56.
I apologize for any previous inconsistencies and thank you for your understanding.
Go step by step to reduce the radical.
square root of, 224, end square root
224
square root of, 4, end square root, dot, square root of, 56, end square root
4
⋅
56
2, square root of, 56, end square root2
56
2, square root of, 4, end square root, dot, square root of, 14, end square root2
4
⋅
14
2, dot, 2, square root of, 14, end square root2⋅2
14
square root of, empty space, end square root
x
Multiply the two numbers in front of the radical.
Keep the inside of the radical the same.