What is the product of 33 and 10, square root of, 28, end square root10
28
in simplest radical form?
To simplify the expression, let's break it down step by step:
Step 1: Calculate the product of 33 and 10.
33 x 10 = 330
Step 2: Simplify the square root of 28.
The square root of 28 can be simplified by factoring out the perfect square. Since 4 is a perfect square that can be found in 28, we can write:
√28 = √(4 x 7)
Next, we can take the square root of 4:
√(4 x 7) = 2√7
Step 3: Final expression
The final expression in simplest radical form is:
330√7
To find the product of 33 and (square root of 28 + square root of 10), we can follow these steps:
Step 1: Simplify the square root of 28 and 10
The square roots of 28 and 10 can be simplified as follows:
Square root of 28 = square root of (4 * 7) = 2 * square root of 7
Square root of 10 = square root of (2 * 5) = square root of 2 * square root of 5
Step 2: Substitute the simplified values into the expression
Now we can substitute the simplified values into the expression:
33 * (2 * square root of 7 + square root of 2 * square root of 5)
Step 3: Distribute the multiplication
Distribute 33 to each term in the parentheses:
66 * square root of 7 + 33 * square root of 2 * square root of 5
Step 4: Simplify further if possible
If there are any like terms, combine them:
66 * square root of 7 + 33 * square root of 2 * square root of 5
Step 5: Finalize the answer
The final product is 66 * square root of 7 + 33 * square root of 2 * square root of 5, which is in its simplest radical form.
To find the product of 33 and 10, simply multiply the two numbers together:
33 * 10 = 330
To find the square root of 28, start by determining if there are any perfect square factors of 28. The factors of 28 are 1, 2, 4, 7, 14, and 28. Since 4 is a perfect square factor of 28, it can be factored out as:
√(4 * 7)
Taking the square root of 4 gives:
2√7
Finally, to find the square root of 10, determine if there are any perfect square factors of 10. The factors of 10 are 1 and 10. Since there are no perfect square factors, the square root of 10 is:
√10
Combining all the parts together, the expression becomes:
330 * 2√7 * √10
To simplify this expression, multiply the coefficients together:
330 * 2 = 660
The simplified expression can now be written as:
660√7√10
However, it is preferable to consolidate the square root terms. Since multiplying two square root terms together is the same as taking the square root of their product, the expression can be further simplified:
660√(7 * 10)
Multiplying 7 and 10 gives:
660√70
Therefore, the product of 33 and 10, square root of 28, square root 10 in simplest radical form is:
660√70.
give me the simplest form there is
I apologize for the previous incorrect response. Let's simplify the expression correctly:
To find the product of 33 and (square root of 28 + square root of 10), we can follow these steps:
Step 1: Simplify the square root of 28 and 10:
The square root of 28 can be simplified as 2√7.
The square root of 10 remains as √10.
Step 2: Substitute the simplified values into the expression:
33 * (2√7 + √10)
Step 3: Distribute the multiplication:
(33 * 2√7) + (33 * √10)
This gives us:
66√7 + 33√10
So, the simplest form of the expression is:
66√7 + 33√10.