Question

What is the simplified form of 400 x^ 100?

200x ^ 10
200x ^ 50
20x ^ 10
20x ^ 50

Answer 1

Answer and Step-by-step explanation:

√
`400` × √
`100`
`=40,000`

√
`40,000=200`

`Thus,~the~first~option~is~correct.`

Answer 2

Answer: The correct option is

(D)
`20x^(50).`

Step-by-step explanation: We are given to find the simplified form of the following radical expression :

`E=\sqrt{400x^(100)}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be using the following properties :

`(i)~(ab)^c=a^cb^c,\\\\(ii)~√(a^b)=a^{(b)/(2)}.`

From expression (i), we get

`E\\\\=\sqrt{400x^(100)}\\\\=\sqrt{(20x^(50))^2}\\\\=(20x^(50))^(2)/(2)\\\\=20x^(50).`

Thus, the required simplified form of the given expression is
`20x^(50).`

Option (D) is CORRECT.