Question

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

Answer 1

Answer:

$125\sqrt[4]{8}$

Explanation:

A number of the form

$a^{\frac{m}{n}}$

can be re-written in the radical form as follows:

$\sqrt[n]{a^m}$

In this problem, we have:

a = 1,250

m = 3

n = 4

So, if we apply the formula, we get

$1,250^{\frac{3}{4}}=\sqrt[4]{(1,250)^3}$

Then, we can rewrite 1250 as

$1250 = 2\cdot 5^4$

So we can rewrite the expression as

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

Answer 2

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.