Question

9√(300m^2n^3p^4).
A. 30mn^2√3p
B. 90mn^3√2p
C. 30m^2np^2√3
D. 90m^2n^3p^2√3

Answer 1

The expression 9√(300m^2n^3p^4) simplifies to 90mnp^2n^2√(3) after factoring 300 into primes, pairing and taking out the squares of the variables and the number 2 and 5, and finally multiplying by the coefficient 9.

Step-by-step explanation:

To simplify the expression 9√(300m2n3p4), we first need to break down 300 into its prime factors and simplify the variables under the radical.

The prime factoring of 300 is 2 * 2 * 3 * 5 * 5. We can pair the squares of factors to move them outside the radical, leaving the unpaired factors inside. The expression inside the radical becomes 22 * 3 * 52 * m2 * n3 * p4, which simplifies to 10m1n1p2√(3n) outside the radical.

Now, we multiply this by the coefficient 9 outside the radical to get 90mn1p2√(3n).

Observing that n1 is under the radical and we have n3 in the original expression, we take out an n2 pair, leaving an n inside the radical.

Finally, we have 90mnp2n2√(3), which corresponds to option B in the question.