Question

When 1,250 Superscript three-fourths is written in simplest radical form, which value remains under the radical?

Answer 1

The value remains under the radical is 8 ⇒ last answer

Step-by-step explanation:

Let us revise how to write the exponent as a radical

• $a^{\frac{m}{n}}$ can be written as $\sqrt[n]{a^{m}}$
• To simplify the radical factorize the base "a" to its prime factors

Example:

• $(54)^{\frac{2}{3}}=\sqrt[3]{(54)^{2}}$ ,
• Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 = $2(3)^{3}$
• $\sqrt[3]{(54)^{2}}=\sqrt[3]{[2(3^{3}]^{2}}=\sqrt[3]{2^{2}*3^{6}}$
• 2² can not go out the radical because 2 is less than 3 not divisible by 3
• $3^{6}$ can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical
• $\sqrt[3]{(54)^{2}}=3^{2}\sqrt[3]{2^{2}}=9\sqrt[3]{4}$

Now let us solve your problem

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

- Factorize 1250 to its prime factors

∵ 1250 = 2 × 5 × 5 × 5 × 5

∴ $1250=2*5^{4}$

∴ $\sqrt[4]{(2*5^{4})^{3}}=\sqrt[4]{2^{3}*5^{12}}$

∵ 2³ can not go out the radical because 3 < 4 and not divisible by it

- $5^{12}$ can go out the radical because 12 can divided by 4

∵ 12 ÷ 4 = 3

∴ $5^{12}$ can go out the radical as 5³

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

∴ $\sqrt[4]{1250}=125\sqrt[4]{8}$

∴ The value remains under the radical = 8

The value remains under the radical is 8

Learn more:

You can learn more about the radicals in brainly.com/question/7153188

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