Question

When 1,250^3/4 is written in simplest radical form, which value remains under the radical?

Answer 1

Answer: The value remains under the radical is 8.

Explanation:

Given that,

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

We know that,

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

Here, n = integer number

n is greater than x.

a = real number

Therefore,

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

$1250^{\frac{3}{4}}=\sqrt[4]{2.5^{4}}^3$

$1250^{\frac{3}{4}}=5^3\sqrt[4]{2}^3$

$1250^{\frac{3}{4}}=125\sqrt[4]{8}$

Hence, The value remains under the radical is 8.

Answer 2

Based on the steps of simplifying numbers, the value which remains under the radical after simplifying is 8.

When 1,250^3/4 is written in simplest radical form, which value remains under the radical?

In simplifying the expression, the following steps are taken:

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

1250^3/4 = $\sqrt[4]({2 * 5^4} )^3$

1250^3/4 = $5^3 * \sqrt[4]{2^3}$

1250^3/4 = $125 * \sqrt[4]{8}$

Therefore, the value which remains under the radical after simplifying is 8.

Learn more about simplification of numbers at: https://brainly.com/question/481658