Question

Solve 16pq² = 25 for q.

q=±5√p/4
q=±5√p/4p
q=±√5p/4p
q=±√5p/4

Answer 1

remember
√(ab)=(√a)(√b)
and
√(a/b)=(√a)/(√b)

divide both sides by 16p

q²=25/(16p)
sqrt both sides
remember positive and negative roots

`q= (+/-5)/(4 √(p) )`
rationalize denom by multiplying by (√p)/(√p)

`q= (+/-5√(q))/(4 p )`

2nd option is correct

Answer 2

Option 2 is correct

Explanation:

Given the equation

`16pq^2=25`

we have to solve the above equation for q

`16pq^2=25`

Divide by 16p both sides, we get

`(16pq^2)/(16p)=(25)/(16p)`

`q^2=(25)/(16p)`

Taking square root on both sides

`q=\pm(√(25))/(√(16p))=\pm(5)/(4\sqrt p)`

Rationalizing, we get

`q=\pm(5)/(4\sqrt p)* (\sqrt p)/(\sqrt p)=\pm(5\sqrtp)/(4p)`

Option 2 is correct