Question

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

Answer 1

Answer: 8

Step-by-step explanation:

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

Answer 2

Answer:

The value remains under the radical is 8.

Step-by-step 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 $1250^{\frac{3}{4}}$

Applying property,

$a^{\frac{x}{n}}=n\sqrt{a^x}$

So, $1250^{\frac{3}{4}}$

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

$=\sqrt[4]{1250\times 1250\times 1250}$

$=\sqrt[4]{5^4(2)\times 5^4(2)\times 5^4(2)}$

$=5\times 5\times 5\sqrt[4]{2^3}$

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

Therefore, The value remains under the radical is 8.