Question

Simplify the following expression

Answer 1

The answer is

`4 {c}^(2) {d}^(2) √(10c)`

Explanation:

`\sqrt{160 {c}^(5) {d}^(4) }`

To solve the expression, expand the terms

That's

`\sqrt{ {4}^(2) * 10 {c}^(4) * {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) } * \sqrt{ {c}^(4) } * \sqrt{ {d}^(4) } * √(10c)`

Reduce the surds

Thats

`\sqrt{ {4}^(2) } = 4 \\ \sqrt{ {c}^(4) } = {c}^(2) \\ \sqrt{ {d}^(4) } = {d}^(2)`

We have

`4 * {c}^(2) * {d}^(2) * √(10c)`

We have the final answer as

`4 {c}^(2) {d}^(2) √(10c)`

Hope this helps you

Answer 2

See below

Explanation:

√160c⁵d⁴

= √160 * √c⁵ * √d⁴

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

= 4 * √10 * c * c * √c * d * d

= 4c²d²√10c