Question

select the correct answer.
which expression is equivalent to $4x^{2}\sqrt{5x^{4}} \cdot 3\sqrt{5x^{8}}$, if $x \
eq 0$
a. $12x^{10}\sqrt{5}$
b. $60x^{8}$
c. $35x^{18}$
d. $7x^{10}\sqrt{5}$

Explanation:

Step1: Multiply coefficients outside roots

$4 \times 3 = 12$

Step2: Multiply terms inside square roots

$\sqrt{5x^4} \times \sqrt{5x^8} = \sqrt{5 \times 5 \times x^4 \times x^8} = \sqrt{25x^{12}}$

Step3: Simplify the square root

$\sqrt{25x^{12}} = 5x^6$

Step4: Multiply with $x^2$ and coefficient

$12 \times x^2 \times 5x^6 = 60x^{2+6} = 60x^8$

Answer:

B. $60x^8$