if the square root of twice a number is diminished by three, the result is 5. what is the number?
√2x - 3 = 5
Solve for x.
x=32
To find the number, let's break down the information provided step by step.
1. Let's denote the number as "x".
2. "The square root of twice a number" can be represented as √(2x).
3. "Diminished by three" means subtracting 3 from √(2x). So, we have √(2x) - 3.
4. The result is given as 5. So, we set up the equation √(2x) - 3 = 5.
5. To solve for x, we need to isolate √(2x) by adding 3 to both sides of the equation: √(2x) = 5 + 3.
This simplifies to √(2x) = 8.
Now, to eliminate the square root (√), we need to square both sides. Squaring both sides of the equation yields:
(√(2x))^2 = 8^2
2x = 64
Divide both sides by 2 to solve for x:
2x / 2 = 64 / 2
x = 32
Therefore, the number is 32.