The square root of twice a number is equal to one-half of that number. Find the number.
8
8*2 = 16, square root of 16 is 4.
1/2 of 8 is also 4, therefore the answer is 8.
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To find the number, let's first represent the number as x. We are given that the square root of twice the number is equal to one-half of that number.
So, we can write the equation as:
√(2x) = (1/2)x
To solve this equation, let's isolate the square root term by squaring both sides:
(√(2x))^2 = ((1/2)x)^2
Simplifying, we have:
2x = (1/4)x^2
Now, let's rearrange the equation to bring all the terms to one side:
0 = (1/4)x^2 - 2x
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1/4, b = -2, and c = 0. Plugging these values into the formula:
x = (-(-2) ± √((-2)^2 - 4(1/4)(0))) / (2(1/4))
Simplifying further:
x = (2 ± √(4 - 0)) / (1/2)
x = (2 ± 2) / (1/2)
Now, we have two possible solutions:
1) x = (2 + 2) / (1/2) = 4 / (1/2) = 4 * 2 = 8
2) x = (2 - 2) / (1/2) = 0 / (1/2) = 0
Therefore, the number could be either 8 or 0.