Question

When 1250 to the 3/4 power is written in simplest radical form, which value remains under the radical?

Answer 1

Answer: 8

Explanation:

`1250^{(3)/(4)}=\sqrt[4]{1250^3} \\\\= \sqrt[4]{1250\cdot 1250\cdot1250} \\\\= \sqrt[4]{5^4(2)\cdot 5^4(2)\cdot5^4(2)} \\\\=5\cdot5\cdot5\sqrt[4]{2^3} \\\\=125\sqrt[4]{8}`

Answer 2

The value remains under the radical is 8.

Explanation:

Given : When 1250 to the 3/4 power is written in simplest radical form.

To find : Which value remains under the radical?

Solution :

The expression is written as
`1250^{(3)/(4)}`

Applying property,

`a^{(x)/(n)}=n√(a^x)`

So,
`1250^{(3)/(4)}`

`=\sqrt[4]{1250^3}`

`=\sqrt[4]{1250* 1250* 1250}`

`=\sqrt[4]{5^4(2)* 5^4(2)* 5^4(2)}`

`=5* 5* 5\sqrt[4]{2^3}`

`=125\sqrt[4]{8}`

Therefore, The value remains under the radical is 8.