Question

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

Answer 1

Answer: Simplifying

x2 + 400x + -40000 = 0

Reorder the terms:

-40000 + 400x + x2 = 0

Solving

-40000 + 400x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40000' to each side of the equation.

-40000 + 400x + 40000 + x2 = 0 + 40000

Reorder the terms:

-40000 + 40000 + 400x + x2 = 0 + 40000

Combine like terms: -40000 + 40000 = 0

0 + 400x + x2 = 0 + 40000

400x + x2 = 0 + 40000

Combine like terms: 0 + 40000 = 40000

400x + x2 = 40000

The x term is 400x. Take half its coefficient (200).

Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.

400x + 40000 + x2 = 40000 + 40000

Reorder the terms:

40000 + 400x + x2 = 40000 + 40000

Combine like terms: 40000 + 40000 = 80000

40000 + 400x + x2 = 80000

Factor a perfect square on the left side:

(x + 200)(x + 200) = 80000

Calculate the square root of the right side: 282.842712475

Break this problem into two subproblems by setting

(x + 200) equal to 282.842712475 and -282.842712475.

Subproblem 1

x + 200 = 282.842712475

Simplifying

x + 200 = 282.842712475

Reorder the terms:

200 + x = 282.842712475

Solving

200 + x = 282.842712475

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-200' to each side of the equation.

200 + -200 + x = 282.842712475 + -200

Combine like terms: 200 + -200 = 0

0 + x = 282.842712475 + -200

x = 282.842712475 + -200

Combine like terms: 282.842712475 + -200 = 82.842712475

x = 82.842712475

Simplifying

x = 82.842712475

Subproblem 2

x + 200 = -282.842712475

Simplifying

x + 200 = -282.842712475

Reorder the terms:

200 + x = -282.842712475

Solving

200 + x = -282.842712475

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-200' to each side of the equation.

200 + -200 + x = -282.842712475 + -200

Combine like terms: 200 + -200 = 0

0 + x = -282.842712475 + -200

x = -282.842712475 + -200

Combine like terms: -282.842712475 + -200 = -482.842712475

x = -482.842712475

Simplifying

x = -482.842712475

Solution

The solution to the problem is based on the solutions

from the subproblems.

x = {82.842712475, -482.842712475}

Answer 2

200√5

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.