Answer :
the simplification of the product surd [tex]\sqrt[3]{12x^{4} }[/tex]×[tex]\sqrt[3]{3x^{8} }[/tex] is 3x⁴
What is a surd?
Surds are the values in square root that cannot be further simplified into whole numbers or integers.
To simplify the product below, we need to use the law of surd.
Recall from the law of surd,
- √a×√b = √ab
Given the product surd,
- [tex]\sqrt[3]{12x^{4} }[/tex]×[tex]\sqrt[3]{3x^{8} }[/tex]
Applying the law of Surd we have
- [tex]\sqrt[3]{(9*3)(x^{4}*x^{8}) }[/tex]
- [tex]\sqrt[3]{27x^{12} }[/tex]
- [tex]\sqrt[3]{27} * \sqrt[3]{x^{12} }[/tex]
- 3x⁴
Hence, the simplification of [tex]\sqrt[3]{12x^{4} }[/tex]×[tex]\sqrt[3]{3x^{8} }[/tex] is 3x⁴
Learn more about surd here: https://brainly.com/question/840021
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