Question

simplify the following expression

Answer 1

Answer:

See below

Step-by-step explanation:

√160c⁵d⁴

= √160 * √c⁵ * √d⁴

= √16 * √10 * √c² * √c² * √c * √d² * √d²

= 4 * √10 * c * c * √c * d * d

= 4c²d²√10c

Answer 2

Answer:

The answer is

$4 {c}^{2} {d}^{2} \sqrt{10c}$

Step-by-step explanation:

$\sqrt{160 {c}^{5} {d}^{4} }$

To solve the expression, expand the terms

That's

$\sqrt{ {4}^{2} \times 10 {c}^{4} \times {cd}^{4} }$

Using the rule

The square root of a product is equal to the product of the roots of each factor.

Expand

That's

$\sqrt{ {4}^{2} } \times \sqrt{ {c}^{4} } \times \sqrt{ {d}^{4} } \times \sqrt{10c}$

Reduce the surds

Thats

$\sqrt{ {4}^{2} } = 4 \\ \sqrt{ {c}^{4} } = {c}^{2} \\ \sqrt{ {d}^{4} } = {d}^{2}$

We have

$4 \times {c}^{2} \times {d}^{2} \times \sqrt{10c}$

We have the final answer as

$4 {c}^{2} {d}^{2} \sqrt{10c}$

Hope this helps you