Simplify each expression. All variables represent positive numbers.
Sqrt of 75p^3q^2 divide by sqrt of p^5q^4
My answer:
5q sqrt of 3 / p^2q^2
Is this right?
Not quite.
√(75p^3q^2) = 5√3 pq√p
√(p^5q^4) = p^2q^2 √p
divide and you end up with (5√3)/(pq)
Hmm. I guess you could have meant
5√(3/(p^2q^2))
but that simplifies to my result above
To simplify the expression
√(75p^3q^2) / √(p^5q^4),
you need to simplify the numerator and the denominator separately, and then divide the two simplified expressions.
For the numerator, you can simplify √(75p^3q^2) by separating the factors inside the square root:
√(75p^3q^2) = √(25 · 3 · p^2 · p · q^2)
Next, take out any perfect squares from under the square root:
√(75p^3q^2) = 5p√(3p)q
Moving on to the denominator, you have √(p^5q^4). Again, separate the factors under the square root:
√(p^5q^4) = √(p^4 · p · q^4)
Take out any perfect squares:
√(p^5q^4) = p^2q^2√(p)
Now, you can simplify the expression by dividing the simplified numerator by the simplified denominator:
(5p√(3p)q) / (p^2q^2√(p))
You can cancel out common factors if they appear in the numerator and the denominator:
(5√(3p)) / (p√(p))
Therefore, the simplified expression is:
(5√(3p)) / (p√(p))
Now, compare this to your answer and see if they match.