IDNLearn.com offers a unique blend of expert answers and community insights. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.
Sagot :
The quotient of [tex]20\sqrt{z^{6} }[/tex] ÷ [tex]\sqrt{16z^{7} }[/tex] in simplest radical form is [tex]\frac{5\sqrt{z} }{z}[/tex].
How to express a simplest radical form?
Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.
Given
[tex]20\sqrt{z^{6} }[/tex] ÷ [tex]\sqrt{16z^{7} }[/tex]
Rewrite as fraction: [tex]\frac{20\sqrt{z^{6} } }{\sqrt{16z^{7} } }[/tex]
Factor and rewrite the radicand in exponential form: [tex]\frac{20\sqrt{z^{6} } }{\sqrt{4^{2}. z^{6} .z} }[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex] :
= [tex]\frac{20\sqrt{z^{6} } }{\sqrt{4^{2} .\sqrt{z^{6}.\sqrt{z} } } }[/tex]
Simply the radical expression, we get:
= [tex]\frac{20z^{3} }{4z^{3}\sqrt{z} }[/tex]
Reduce fraction to the lowest term by canceling the greater common factor, we get
= [tex]\frac{5}{\sqrt{z} }[/tex]
Rationalize the denominator
= [tex]\frac{5\sqrt{z} }{\sqrt{z} .\sqrt{z} }[/tex]
= [tex]\frac{5\sqrt{z} }{z}[/tex]
Hence, the quotient of [tex]20\sqrt{z^{6} }[/tex] ÷ [tex]\sqrt{16z^{7} }[/tex] in simplest radical form is [tex]\frac{5\sqrt{z} }{z}[/tex].
Find out more information about simplest radical form here
https://brainly.com/question/12966955
#SPJ3
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.
