PrincessMaxx
Answered

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

Verified Answer :

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.

mickymike92

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

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