Express in simplest radical form.
square root of, 32, end square root
32
sqrt(32) = sqrt(16*2) = sqrt(16) * sqrt(2) = 4sqrt(2)
To express the square root of 32 in simplest radical form, we need to find any perfect square factors of 32.
First, let's break down 32 into its prime factorization:
32 = 2 * 2 * 2 * 2 * 2 = 2^5
Now, let's group the prime factors in pairs:
32 = (2 * 2) * (2 * 2) * 2 = 4 * 4 * 2
Since 4 is a perfect square, we can simplify the square root of 32 as follows:
√32 = √(4 * 4 * 2) = √(4^2 * 2) = 4√2
So, the simplest radical form of the square root of 32 is 4√2.
To express the square root of 32 in simplest radical form, we need to find the largest perfect square that divides into 32.
Let's break down 32 into its prime factors:
32 = 2 * 2 * 2 * 2 * 2 = 2^5
Now, let's group the prime factors in pairs inside a square root:
√(2^5) = √(2 * 2 * 2 * 2 * 2)
Since each pair of the prime factor represents a perfect square (2 * 2 = 4), we can simplify the expression:
√(2 * 2 * 2 * 2 * 2) = 2 * 2 * √(2) = 4√(2)
Therefore, the square root of 32 in simplest radical form is 4√(2).
can I have the answer more understanding
Sure! I apologize for any confusion. Let's break it down step by step.
To express the square root of 32 in simplest radical form, we need to find the largest perfect square that divides into 32 without leaving a remainder.
To do this, we can start by finding the prime factors of 32. Prime factors are the numbers that divide evenly into a given number without leaving a remainder.
The prime factors of 32 are 2, 2, 2, 2, and 2. We can write this as 2^5, which means 2 multiplied by itself 5 times.
Now, let's group the prime factors in pairs to see if we have any perfect squares. We pair them as follows:
2 * 2 = 4
2 * 2 = 4
Now, we have two pairs of 2s, which can be simplified to the perfect square of 4. We can write this as (2 * 2) * (2 * 2) = 4 * 4 = 16.
So, we have simplified the expression 32 as 16 * 2.
Taking the square root of 16, we get √16 = 4. The 2 remains under the square root since it is not a perfect square.
Putting it all together, we have:
√32 = √(16 * 2) = √16 * √2 = 4√2
Therefore, the square root of 32 in simplest radical form is 4√2.
Express in simplest radical form.
square root of, 125, end square root
125
To express the square root of 125 in simplest radical form, we need to find any perfect square factors of 125.
125 can be written as 5 * 5 * 5 = 5^3.
Since there are no pairs of perfect squares in the prime factorization of 125, we cannot simplify it further.
Therefore, the simplest radical form of the square root of 125 is √125.
Can u give it to me more understanding
Sure! I apologize for any confusion. Let's break it down step by step.
To express the square root of 125 in simplest radical form, we need to find any perfect square factors of 125.
Let's start by finding the prime factors of 125. Prime factors are the numbers that divide evenly into a given number without leaving a remainder.
The prime factors of 125 are 5, 5, and 5. We can write this as 5^3, which means 5 multiplied by itself 3 times.
Now, let's group the prime factors in pairs to see if we have any perfect squares. We pair them as follows:
5 * 5 = 25
Since we have a pair of 5s, we can simplify it to the perfect square of 25.
So, we have simplified the expression 125 as 25 * 5.
Taking the square root of 25, we get √25 = 5. The 5 remains under the square root since it is not a perfect square.
Putting it all together, we have:
√125 = √(25 * 5) = √25 * √5 = 5√5
Therefore, the square root of 125 in simplest radical form is 5√5.