What is the product of 88 and 8, square root of, 32, end square root8
32
in simplest radical form?
The product of 88 and 8 is 704.
To simplify the square root of 32, we need to find the largest perfect square that is a factor of 32. The largest perfect square that can be a factor of 32 is 16, since √16 = 4.
Thus, we can simplify the square root of 32 as √32 = √(16 * 2) = √16 * √2 = 4√2.
The final expression is 704 * 4√2 = 2816√2. Therefore, the product of 88 and √32 in simplest radical form is 2816√2.
To find the product of 88 and 8, we simply multiply the two numbers together. So, 88 multiplied by 8 equals 704.
To find the square root of 32, we need to determine the largest perfect square that can be obtained from 32. In this case, it is 16 because 16 multiplied by 2 is equal to 32.
So, the square root of 32 can be written as the square root of 16 multiplied by 2, which simplifies to 4 multiplied by the square root of 2.
Lastly, we have the square root of 8. We can simplify this by determining the largest perfect square that can be obtained from 8, which is 4, because 4 multiplied by 2 is equal to 8.
Thus, the square root of 8 can be written as 2 multiplied by the square root of 2.
Combining these simplified square roots, we have:
Square root of 32 = 4 * square root of 2
Square root of 8 = 2 * square root of 2
Therefore, the expression in simplest radical form is:
704 * square root of 32 * square root of 8
This can be further simplified as:
704 * (4 * square root of 2) * (2 * square root of 2)
Simplifying the expression:
704 * 4 * 2 * (square root of 2 * square root of 2)
Finally, multiplying these numbers together:
704 * 4 * 2 * 2 = 11,264
Thus, the product of 88 and 8, square root of 32, square root of 8, in simplest radical form is 11,264.
To find the product and the square root in simplest radical form, let's break down your question into steps:
Step 1: Find the product of 88 and 8.
88 multiplied by 8 is equal to 704. So, the product of 88 and 8 is 704.
Step 2: Calculate the square root of 32.
The square root (√) of 32 can be simplified by factoring it.
32 can be factored as 16 × 2 = 4 × 4 × 2.
Taking the square root, we can simplify this as √(4 × 4 × 2) = √16 × √2 = 4√2.
So, the square root of 32 is 4√2.
Step 3: Simplify the square root of 8.
The square root (√) of 8 can be simplified by factoring it.
8 can be factored as 4 × 2.
Taking the square root, we can simplify this as √(4 × 2) = √4 × √2 = 2√2.
So, the square root of 8 is 2√2.
Putting it all together, the expression "the product of 88 and 8, square root of 32, square root 8" simplifies to:
704√2√2,
which further simplifies to:
704(2)√2,
and finally simplifies to:
1408√2.
Therefore, the product of 88 and 8, square root of 32, and square root of 8 in simplest radical form is 1408√2.