Answer:
[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]
Step-by-step explanation:
step 1;-
Given [tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} }[/tex]
now you have rationalizing denominator (i.e monomial) with
[tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} } X \frac{\sqrt[3]{(12 y^2 z)^{2} } }{\sqrt[3]{(12 y^2 z)^2} }[/tex]
By using algebraic formula is
- [tex]\sqrt{ab} = \sqrt{a} \sqrt{b}[/tex]......(a)
- now [tex]\frac{\sqrt[3]{5 x^2)(12 y^2 z)^2} }{\sqrt[3]{12 y^2 z)(12 y^2 z)^2} }[/tex]
- [tex]\frac{\sqrt[3]{720 x^2 y^4 z^2} }{\sqrt[3]{(12 y^2 z)^{3} } }[/tex]....(1)
- again using Formula [tex]\sqrt[n]{a^{n} } =a[/tex]
now simplification , we get denominator function
- [tex]\frac{\sqrt[3]{720 x^2 y^4 z^2} }{12 y^2 z}[/tex]
again you have to simplify numerator term
- [tex]\frac{\sqrt[3]{2^3 y^3 90 (x^2 y z^2)} }{12 y^2 z}[/tex]
now simplify
- [tex]\frac{2 y\sqrt[3]{90 x^2 y z^2} }{12 y^2 z}[/tex]
cancelling y and 2 values
we get Final answer
[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]
