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lilavasa [31]
3 years ago
10

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

Mathematics
1 answer:
Dvinal [7]3 years ago
8 0

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

#LearnwithBrainly

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Step-by-step explanation:

Given the sequence

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