Answer:
The answer is
[tex]4 {c}^{2} {d}^{2} \sqrt{10c}[/tex]
Step-by-step explanation:
[tex] \sqrt{160 {c}^{5} {d}^{4} } [/tex]
To solve the expression, expand the terms
That's
[tex] \sqrt{ {4}^{2} \times 10 {c}^{4} \times {cd}^{4} } [/tex]
Using the rule
The square root of a product is equal to the product of the roots of each factor.
Expand
That's
[tex] \sqrt{ {4}^{2} } \times \sqrt{ {c}^{4} } \times \sqrt{ {d}^{4} } \times \sqrt{10c} [/tex]
Reduce the surds
Thats
[tex] \sqrt{ {4}^{2} } = 4 \\ \sqrt{ {c}^{4} } = {c}^{2} \\ \sqrt{ {d}^{4} } = {d}^{2} [/tex]
We have
[tex]4 \times {c}^{2} \times {d}^{2} \times \sqrt{10c} [/tex]
We have the final answer as
[tex]4 {c}^{2} {d}^{2} \sqrt{10c} [/tex]
Hope this helps you
