Find the square root of 45: √45.
13 answers
The square root of 45 (denoted as √45) is approximately 6.708.
Find the square root of 175: √175. If it makes sense, put it into a separate square root - like how √45 square rooted is equal to 3√5.
To find the square root of 175 (denoted as √175), we can simplify it further by breaking it down into its prime factors.
The prime factorization of 175 is 5 * 5 * 7, or 5^2 * 7.
√175 can then be written as √(5^2 * 7).
Using the property of square roots, we can separate the square root into two separate square roots:
√(5^2) * √7 = 5√7.
Therefore, the square root of 175 (√175) can be simplified as 5√7.
The prime factorization of 175 is 5 * 5 * 7, or 5^2 * 7.
√175 can then be written as √(5^2 * 7).
Using the property of square roots, we can separate the square root into two separate square roots:
√(5^2) * √7 = 5√7.
Therefore, the square root of 175 (√175) can be simplified as 5√7.
Find the square root of 96: √96. Choose the correct answer from below:
6√4
4√6
16√6
24
6√4
4√6
16√6
24
To find the square root of 96 (denoted as √96), we can simplify it further by breaking it down into its prime factors.
The prime factorization of 96 is 2 * 2 * 2 * 2 * 2 * 3, or 2^5 * 3.
Now, let's rewrite √96 using the property of square roots:
√(2^5 * 3)
We can separate this into two separate square roots:
√(2^4 * 2 * 3)
Simplifying further:
2^2 * √(2 * 3)
This can be written as:
4√(2 * 3)
So, the correct answer is 4√6
The prime factorization of 96 is 2 * 2 * 2 * 2 * 2 * 3, or 2^5 * 3.
Now, let's rewrite √96 using the property of square roots:
√(2^5 * 3)
We can separate this into two separate square roots:
√(2^4 * 2 * 3)
Simplifying further:
2^2 * √(2 * 3)
This can be written as:
4√(2 * 3)
So, the correct answer is 4√6
Find the cubic root of 96: ∛96. Choose an answer below.
2∛7
4√6
2√12
2∛12
2∛7
4√6
2√12
2∛12
To find the cubic root of 96 (denoted as ∛96), we can simplify the number by breaking it down into its prime factors.
The prime factorization of 96 is 2 * 2 * 2 * 2 * 2 * 3, or 2^5 * 3.
Now, let's rewrite ∛96 using the property of cubic roots:
∛(2^5 * 3)
We can separate this into two separate cubic roots:
∛(2^3 * 2^2 * 3)
Simplifying further:
2 * 2 * ∛(2 * 3)
This can be written as:
2^2 * ∛(2 * 3)
So, the correct answer is 4∛6
The prime factorization of 96 is 2 * 2 * 2 * 2 * 2 * 3, or 2^5 * 3.
Now, let's rewrite ∛96 using the property of cubic roots:
∛(2^5 * 3)
We can separate this into two separate cubic roots:
∛(2^3 * 2^2 * 3)
Simplifying further:
2 * 2 * ∛(2 * 3)
This can be written as:
2^2 * ∛(2 * 3)
So, the correct answer is 4∛6
Find the cubic root of 189: ∛189. Choose an answer below:
3∛7
9∛21
27∛7
3√7
3∛7
9∛21
27∛7
3√7
To find the cubic root of 189 (denoted as ∛189), we can simplify the number by breaking it down into its prime factors.
The prime factorization of 189 is 3 * 3 * 3 * 7, or 3^3 * 7.
Now, let's rewrite ∛189 using the property of cubic roots:
∛(3^3 * 7)
We can simplify it further:
3 * ∛7
So, the correct answer is 3∛7.
The prime factorization of 189 is 3 * 3 * 3 * 7, or 3^3 * 7.
Now, let's rewrite ∛189 using the property of cubic roots:
∛(3^3 * 7)
We can simplify it further:
3 * ∛7
So, the correct answer is 3∛7.
Find the square root of 250: √250. Choose an answer from below:
5√10
10√5
25√10
250
5√10
10√5
25√10
250
To find the square root of 250 (denoted as √250), we can simplify the number by breaking it down into its prime factors.
The prime factorization of 250 is 2 * 5 * 5 * 5, or 2 * 5^3.
Now, let's rewrite √250 using the property of square roots:
√(2 * 5^3)
We can separate this into two separate square roots:
√2 * √(5^3)
Simplifying further:
√2 * 5√5
So, the correct answer is 5√2 * √5, or more commonly written as 5√10.
The prime factorization of 250 is 2 * 5 * 5 * 5, or 2 * 5^3.
Now, let's rewrite √250 using the property of square roots:
√(2 * 5^3)
We can separate this into two separate square roots:
√2 * √(5^3)
Simplifying further:
√2 * 5√5
So, the correct answer is 5√2 * √5, or more commonly written as 5√10.
Find the square root of 128: √128. Choose an answer from below:
2√4
8√2
√64 x √2
4√2
2√4
8√2
√64 x √2
4√2
To find the square root of 128 (denoted as √128), we can simplify the number by breaking it down into its prime factors.
The prime factorization of 128 is 2 * 2 * 2 * 2 * 2 * 2 * 2, or 2^7.
Now, let's rewrite √128 using the property of square roots:
√(2^7)
We can separate this into two separate square roots:
√(2^6 * 2)
Simplifying further:
2^3 * √2
Which can be written as:
8√2
So, the correct answer is 8√2.
The prime factorization of 128 is 2 * 2 * 2 * 2 * 2 * 2 * 2, or 2^7.
Now, let's rewrite √128 using the property of square roots:
√(2^7)
We can separate this into two separate square roots:
√(2^6 * 2)
Simplifying further:
2^3 * √2
Which can be written as:
8√2
So, the correct answer is 8√2.
1 answer