Evaluate \(\sqrt{\frac{s^2 - (b+c)s + bc}{bc}}\) when \(b=25\), \(c=7\), and \(s=30\).

The expression b c s 2 − ( b + c ) s + b c ​ ​ evaluates to approximately 0.81 when substituting b = 25 , c = 7 , and s = 30 . This is calculated step-by-step by substituting values and simplifying the expression. The final result represents the square root of the ratio derived from the given variables.
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Answered by Anonymous | 2025-07-04

To evaluate b c s 2 − ( b + c ) s + b c ​ ​ with the given values b = 25 , c = 7 , and s = 30 , we should first substitute these values into the expression step-by-step.

Substitute the values: Expression: b c s 2 − ( b + c ) s + b c ​ ​ Substitute b = 25 , c = 7 , s = 30 25 ⋅ 7 3 0 2 − ( 25 + 7 ) ⋅ 30 + 25 ⋅ 7 ​ ​

Calculate inside the numerator first:

3 0 2 = 900
b + c = 25 + 7 = 32 and ( b + c ) s = 32 ⋅ 30 = 960
b c = 25 ⋅ 7 = 175

Substitute back: 900 − 960 + 175 Which simplifies to: 900 − 960 + 175 = 115

Substitute the simplified numerator and calculate the denominator:

b c = 25 ⋅ 7 = 175

Therefore the expression becomes: 175 115 ​ ​

Simplify the fraction:

Divide the numerator and the denominator by their greatest common divisor, which is 5. 175 115 ​ = 175 ÷ 5 115 ÷ 5 ​ = 35 23 ​


Calculate the square root:

The final expression becomes: 35 23 ​ ​



This expression, 35 23 ​ ​ , is the simplified form of the given expression. Since neither 23 nor 35 are perfect squares, this is the simplest rational form of the expression.

Answered by OliviaMariThompson | 2025-07-06