A couple of extra practice questions I can't remember how to do. Can anyone help?
1. "2*squareroot*5(3*squareroot*7 + 8*squareroot*12)"
I simplified down to 6*squareroot*35 + 2*squareroot*15, but now I am stuck!
2. "The sum of a number and the square of that number is 30. What is the number?"
Is the number 900?
Thanks for any help!
Ok
for number one i can't follow your logic, but you have to solve the problem in the brackets before using outside information.
For number 2... The equation would be written like this
n + n squared = 30
therefore what numbers can you square that are below 30?
Work backwards
put in values for n
1,2,3 etc. until you can add the same number and then get thirty
Sure, I can help you with both of these questions. Let's start with the first one:
1. "2*squareroot*5(3*squareroot*7 + 8*squareroot*12)"
You simplified it correctly to 6*squareroot*35 + 2*squareroot*15. However, you can simplify it even further. In order to combine the terms, you need to check if the numbers inside the square roots have any common factors. Let's look at the numbers inside the square roots:
6*squareroot*35 + 2*squareroot*15
The factors of 35 are 5 and 7, while the factors of 15 are 3 and 5. You can factor out the common factor of 5:
5 * (6*squareroot*7) + 5 * (2*squareroot*3)
Now you can distribute the 5:
30 * squareroot*7 + 10 * squareroot*3
So the simplified form of the expression is 30*squareroot*7 + 10*squareroot*3.
Now let's move on to the second question:
2. "The sum of a number and the square of that number is 30. What is the number?"
To solve this problem, you need to set up an equation based on the information given. Let's call the number "x". According to the problem, the sum of the number and its square is 30:
x + x^2 = 30
Now you have a quadratic equation. To solve it, you want to rearrange the equation so that it is in standard quadratic form (ax^2 + bx + c = 0). In this case, you need to move all terms to one side of the equation:
x^2 + x - 30 = 0
Now you can factor the quadratic equation:
(x + 6)(x - 5) = 0
Setting each factor equal to zero gives you two possible solutions:
x + 6 = 0 or x - 5 = 0
Solving these equations gives you:
x = -6 or x = 5
So the possible values of the number are -6 and 5. Therefore, the number could be either -6 or 5, but we would need more information to determine which one is correct.
I hope this helps! Let me know if you have any further questions.