MATH SOLVE

6 months ago

Q:
# When 1,250 Superscript three-fourths is written in simplest radical form, which value remains under the radical?2568

Accepted Solution

A:

The value remains under the radical is 8 ⇒ last answerStep-by-step explanation:Let us revise how to write the exponent as a radical[tex]a^{\frac{m}{n}}[/tex] can be written as [tex]\sqrt[n]{a^{m}}[/tex]To simplify the radical factorize the base "a" to its prime factorsExample: [tex](54)^{\frac{2}{3}}=\sqrt[3]{(54)^{2}}[/tex] , Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 = [tex]2(3)^{3}[/tex][tex]\sqrt[3]{(54)^{2}}=\sqrt[3]{[2(3^{3}]^{2}}=\sqrt[3]{2^{2}*3^{6}}[/tex]2² can not go out the radical because 2 is less than 3 not divisible by 3[tex]3^{6}[/tex] can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical[tex]\sqrt[3]{(54)^{2}}=3^{2}\sqrt[3]{2^{2}}=9\sqrt[3]{4}[/tex]Now let us solve your problem∵ [tex]1250^{\frac{3}{4}}=\sqrt[4]{1250^{3}}[/tex]- Factorize 1250 to its prime factors∵ 1250 = 2 × 5 × 5 × 5 × 5∴ [tex]1250=2*5^{4}[/tex]∴ [tex]\sqrt[4]{(2*5^{4})^{3}}=\sqrt[4]{2^{3}*5^{12}}[/tex]∵ 2³ can not go out the radical because 3 < 4 and not divisible by it- [tex]5^{12}[/tex] can go out the radical because 12 can divided by 4∵ 12 ÷ 4 = 3∴ [tex]5^{12}[/tex] can go out the radical as 5³∴ [tex]\sqrt[4]{1250}=5^{3}\sqrt[4]{2^{3}}[/tex]∴ [tex]\sqrt[4]{1250}=125\sqrt[4]{8}[/tex]∴ The value remains under the radical = 8The value remains under the radical is 8Learn more:You can learn more about the radicals in brainly.com/question/7153188#LearnwithBrainly