Question 13

b = 45

To find the value of b, we start with the equation sqrt(b) - sqrt(5) = sqrt(20). By isolating sqrt(b), we can square both sides to solve for b.

A) 25

If b = 25, then sqrt(b) = 5. Substituting this back into the equation gives us 5 - sqrt(5) = sqrt(20). However, sqrt(20) equals 2sqrt(5), and 5 - sqrt(5) does not equal 2sqrt(5), making this option incorrect.

B) 40

If b = 40, then sqrt(b) = sqrt(40), which simplifies to 2sqrt(10). Plugging this back into the equation results in 2sqrt(10) - sqrt(5) = sqrt(20). Since sqrt(20) simplifies to 2sqrt(5), and 2sqrt(10) - sqrt(5) does not equal 2sqrt(5), this option is also incorrect.

C) 45

If b = 45, then sqrt(b) = 3sqrt(5). Substituting this value into the equation gives us 3sqrt(5) - sqrt(5) = sqrt(20). This simplifies to 2sqrt(5) = sqrt(20), which holds true, confirming that this option is correct.

D) 100

If b = 100, then sqrt(b) = 10. Substituting this value back into the equation yields 10 - sqrt(5) = sqrt(20). However, since sqrt(20) equals 2sqrt(5), 10 - sqrt(5) does not equal 2sqrt(5), thus making this option incorrect.

Conclusion

The correct answer is C) 45, as it satisfies the equation sqrt(b) - sqrt(5) = sqrt(20) perfectly. All other options fail to fulfill the equation conditions, confirming that they are not valid solutions.