Correct Question: Find the simplified product: [tex] \sqrt{2x^3}*\sqrt{18x^5} [/tex]
Answer:
[tex] 6x^4 [/tex]
Step-by-step explanation:
Based on the rules of radicals, since [tex] \sqrt{2x^3} [/tex] and [tex] \sqrt{18x^5} [/tex] has the same index (square root), therefore:
[tex] \sqrt{2x^3}*\sqrt{18x^5} = \sqrt{2x^3 * 18x^5} [/tex]
To simplify this, multiply their bases together, and add their exponents.
[tex] = \sqrt{2*18x^{3+5} [/tex]
[tex] = \sqrt{36x^{8} [/tex]
Simplify further
[tex] = \sqrt{36}*\sqrt{x^8} [/tex]
[tex] = \sqrt{6*6}*\sqrt{x^4*x^4} [/tex]
[tex] = 6x^4 [/tex]
