Write the following expression in simplified radical form:2√20×5√40

200√5

Step-by-step explanation:

20 = 2 x 2 x 5

√20 = 2√5

40 = 2 x 2 x 10

√40 = 2√10

2√20

= 2 x 2√5

= 4√5

5√40

= 5 x 2√10

= 10√10

2√20 x 5√40

= 4√5 x 10√10

{ √10 = √5 x √2 }

= 4√5 x 10 x √5 x √2

= 10 x 4 x √2 x √5 x √5

{ √5 x √5 = 5 }

= 10 x 4 x √2 x 5

= 10 x 4 x 5 x √2

= 200√5

Hence simplified.

2 5/8 is the final answer! : )