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
√80 = √(4 * 20)
= √4 * √20
= 2 * √20
= 2√20
= 2√(4 * 5)
= 2 * √4 * √5
= 2 * 2 * √5
= 4√5
To reduce the radical, we can break down the number inside the square root into its prime factors:
Step 1: Find the prime factors of 80:
80 = 2 * 2 * 2 * 2 * 5
Step 2: Group the prime factors in pairs inside the square root:
√(2 * 2 * 2 * 2 * 5)
Step 3: Simplify the pairs:
√(4 * 4 * 5)
Step 4: Take out any pairs with a square number:
√(4 * 4) * √(5)
Step 5: Simplify further:
4 * 2 * √(5)
Step 6: Multiply the numbers outside the square root:
8√5
So, the simplified form of √80 is 8√5.
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To reduce the expression √4 * √20, we can simplify each square root separately:
Step 1: Simplify √4:
√4 = 2
Step 2: Simplify √20:
√20 = √(4 * 5) = 2√5
Step 3: Multiply the simplified square roots:
2 * 2√5 = 4√5
So, the simplified form of √4 * √20 is 4√5.
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If the expression is just √( ), without any number inside, it cannot be simplified further.
So, the simplified form of √( ) is just √( ).
To simplify the radical expression √80, we use the property of radicals that allows us to break down the radicand into its prime factors.
Step 1: Prime factorize the number inside the square root.
The prime factorization of 80 is 2 * 2 * 2 * 2 * 5, which we can write as 2^4 * 5.
Step 2: Group the prime factors into pairs.
We can pair the two twos together as √(2^2 * 2^2 * 5).
Step 3: Bring out the pair of identical factors as a single factor.
Since we have a pair of twos, we can bring them out of the square root sign: 2 * √(2^2 * 5).
Step 4: Simplify the remaining expression inside the square root.
Within the square root, we have 2^2 * 5, which simplifies to 4 * 5, or 20.
Step 5: Combine the factors inside and outside the square root sign.
The simplified expression becomes: 2√20.
Now, using the same steps, let's simplify the expression √4 * √20.
Step 1: Simplify √4.
The square root of 4 is 2.
Step 2: Simplify √20 using the steps mentioned above.
Prime factorizing 20, we get 2 * 2 * 5. Grouping them in pairs, we have √(2^2 * 5). Simplifying, we get 2 * √5.
Step 3: Combine the simplified expressions.
The expression becomes 2 * 2 * √5, which simplifies to 4√5.
Lastly, to simplify the expression √ (blank), we need to know what the value of the blank is. Without a specific number, we cannot simplify it any further.
Therefore, we end up with the expressions: 2√20 and 4√5.
pls give me the right answer
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 √ ( ).
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
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.
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
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.