Solve the question for both the exact irrational root and its rational approximation to the nearest tenth. sqrt 2 over 3 s + 1 = sqrt 23
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To solve the equation sqrt(2)/3 * s + 1 = sqrt(23), we need to isolate the variable 's'. Here's how to do it:
1. Start by subtracting 1 from both sides of the equation:
sqrt(2)/3 * s = sqrt(23) - 1
2. Next, multiply both sides of the equation by 3/sqrt(2) to eliminate the fraction:
(sqrt(2)/3 * s) * (3/sqrt(2)) = (sqrt(23) - 1) * (3/sqrt(2))
Simplifying the left side:
s = (3 * sqrt(2)) / (sqrt(2)/3) = 9
Simplifying the right side:
(sqrt(23) - 1) * (3/sqrt(2)) = ((3(sqrt(23) - 1)) / sqrt(2))
Calculating the value of the right side (approximation to the nearest tenth):
(3(sqrt(23) - 1)) / sqrt(2) ≈ 4.2
Therefore, the exact irrational root (exact value of 's') is 9, and its rational approximation to the nearest tenth is 4.2.