Question

The square root of 1 more than twice a certain number is 5 find the number.

Answer 1

To find the unknown number, set up the equation √(2x + 1) = 5, square both sides to get 2x + 1 = 25, and solve for x, which gives us x = 12.

Step-by-step explanation:

The student is asking for help to find a number where if you take twice the number, add one, and then take the square root, the result will be 5. To solve this, we translate the word problem into a mathematical equation and then solve for the unknown number.

Step-by-Step Solution:

1. Let the unknown number be x.
2. Write down the equation based on the problem: √(2x + 1) = 5.
3. Square both sides to remove the square root: (2x + 1) = 5².
4. Calculate the square of 5: 5² = 25.
5. Replace 5² with 25 in the equation: (2x + 1) = 25.
6. Subtract 1 from both sides: 2x = 24.
7. Divide both sides by 2 to solve for x: x = 24 / 2.
8. The solution is x = 12, which is the number the student is looking for.

This process uses algebraic methods and knowledge of exponents, particularly the concept that squaring a number is the same as raising it to the power of 2, to find the answer.