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.
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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.