3 divided by 5 times the square root of 5 + 3 times the square root of 2. (This problem is written as a fraction.)
Is your problem this:
3 / (5√5 + 3√2)
If so, you need to rationalize the denominator to simplify.
Multiply both top and bottom by (5√5 - 3√2), which is the equivalent of 1, to get rid of the radical in the denominator.
3(5√5 - 3√2) / (5√5 + 3√2)(5√5 - 3√2)
3(5√5 - 3√2) / 107
This is as far as you can go to simplify.
I hope this helps and is what you were asking.
To evaluate the expression 3 divided by 5 times the square root of 5 plus 3 times the square root of 2, we need to follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and simplify step by step.
First, let's simplify the expression within the parentheses.
The expression is: (3 divided by 5) times the square root of 5 plus (3 times the square root of 2).
Step 1: Simplify the division.
3 divided by 5 equals 0.6.
Now the expression becomes: 0.6 times the square root of 5 plus (3 times the square root of 2).
Step 2: Simplify the multiplication.
0.6 times the square root of 5 equals 0.6 * √5 = 0.6√5.
Now the expression becomes: 0.6√5 plus (3 times the square root of 2).
Step 3: Multiply 3 by the square root of 2.
3 times the square root of 2 equals 3√2.
Now the expression becomes: 0.6√5 plus 3√2.
Step 4: Combine like terms.
Since there are no like terms (terms with the same radicand), we cannot simplify further.
Therefore, the final expression is 0.6√5 plus 3√2.