If sqrt(b) - sqrt(5) = sqrt(20), then b =
b = 45.
To solve the equation sqrt(b) - sqrt(5) = sqrt(20), we isolate sqrt(b) and square both sides, ultimately yielding b = 45. This result follows the algebraic manipulations required to eliminate the square roots.
If we substitute b = 25 into the original equation, we find that sqrt(25) - sqrt(5) equals 5 - sqrt(5), which does not equal sqrt(20) (approximately 4.47). Therefore, this choice does not satisfy the given equation.
Substituting b = 40 results in sqrt(40) - sqrt(5), which simplifies to approximately 6.32 - 2.24, yielding about 4.08. This value is not equal to sqrt(20), thus making this option incorrect as well.
When b = 45, we have sqrt(45) - sqrt(5). This can be simplified to 3√5 - √5, which equals 2√5. Since sqrt(20) also simplifies to 2√5, this choice satisfies the equation perfectly, confirming it as the correct answer.
If we take b = 100, then sqrt(100) - sqrt(5) equals 10 - sqrt(5), which does not equal sqrt(20). Thus, this choice fails to satisfy the original equation, making it incorrect.
In solving the equation sqrt(b) - sqrt(5) = sqrt(20), we determined that b must equal 45 for the equation to hold true. The other provided choices do not satisfy the equation, as shown through substitution and simplification. This examination demonstrates the importance of proper algebraic manipulation in finding solutions to square root equations.
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