sqrt(5) * sqrt(10) * sqrt(x^2) =
how can i solev this??
√5*√10*√(x^2)
= √50x
= 5√2x
Ace manufacturing has determined that the cost of labor for producing x transmissions is 0.3x2+400x+550 dollars, while the cost of materials is 0.1x2+50x+800 dollars.
Find the total cost of producing x=500 transmissions.
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To solve the given equation:
1. Simplify each square root individually:
- sqrt(5) = √5
- sqrt(10) = √10
- sqrt(x^2) = x, since the square root of a square is the original number itself.
2. Substitute the simplified square roots back into the equation:
√5 * √10 * x = x√5√10
Note: √5√10 can be further simplified by finding the square root of the product of 5 and 10:
- √(5 * 10) = √50
Therefore, the equation simplifies to:
x√50 = √5 * √10 * x
Now, since both sides of the equation contain x, we can divide both sides by x to isolate the square root term:
x√50/x = (√5 * √10 * x) / x
Simplifying further:
√50 = √5 * √10
Lastly, we can use a calculator to find the square roots:
√50 ≈ 7.071
√5 ≈ 2.236
√10 ≈ 3.162
Hence, the simplified equation is:
7.071 = 2.236 * 3.162
You can use a calculator to evaluate this equation and find the value of x.