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Answer: 2

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  • Answer posted by: myfuzzysticks
    Answer:DStep-by-step explanation:When you have a square root of a number, you essentially have to find a number that can be multiplied by itself to be equivalent to the original number.Take, for example, \sqrt[]{4}. 2 times 2 is 4, meaning that the square root of 4 is 2.Back to the question.2\sqrt[]{18} - 5\sqrt[]{32}First, let's find factors of the numbers that have to be squared.2\sqrt[]{9 * 2} - 5\sqrt[]{16 * 2}Neat! It seems like we already have two squares available!2\sqrt[]{(3 * 3) * 2} - 5\sqrt[]{(4 * 4) * 2}Square 3 and 4:2*3\sqrt[]{2} - 5*4\sqrt[]{2}6\sqrt[]{2} - 20\sqrt[]{2}-14\sqrt[]{2}, Option C.Now, onto the second question.7\sqrt[]{24} + \sqrt[]{90} - 8\sqrt[]{54}Like the first question, let's find some factors7\sqrt[]{4 * 6} + \sqrt[]{9 * 10} - 8\sqrt[]{9 * 6}Aha! Looks like we found a couple more squares!7\sqrt[]{(2*2) * 6} + \sqrt[]{(3*3) * 10} - 8\sqrt[]{(3*3) * 6}Square all of them:7*2\sqrt[]{6} + 3\sqrt[]{10} - 8*3\sqrt[]{6}14\sqrt[]{6} + 3\sqrt[]{10} - 24\sqrt[]{6}Note that you can only add numbers with similar leftover roots, so let's do just that:(14\sqrt[]{6} - 24\sqrt[]{6}) + 3\sqrt[]{10}-10\sqrt[]{6} + 3\sqrt[]{10}, Option D.
  • Answer posted by: TheBreeze
    When you have a square root of a number, you essentially have to find a number that can be multiplied by itself to be equivalent to the original number.Take, for example, [tex]\sqrt[]{4}[/tex]. 2 times 2 is 4, meaning that the square root of 4 is 2.Back to the question.2[tex]\sqrt[]{18}[/tex] - 5[tex]\sqrt[]{32}[/tex]First, let's find factors of the numbers that have to be squared.2[tex]\sqrt[]{9 * 2}[/tex] - 5[tex]\sqrt[]{16 * 2}[/tex]Neat! It seems like we already have two squares available!2[tex]\sqrt[]{(3 * 3) * 2}[/tex] - 5[tex]\sqrt[]{(4 * 4) * 2}[/tex]Square 3 and 4:2*3[tex]\sqrt[]{2}[/tex] - 5*4[tex]\sqrt[]{2}[/tex]6[tex]\sqrt[]{2}[/tex] - 20[tex]\sqrt[]{2}[/tex]-14[tex]\sqrt[]{2}[/tex], Option C.Now, onto the second question.7[tex]\sqrt[]{24}[/tex] + [tex]\sqrt[]{90}[/tex] - 8[tex]\sqrt[]{54}[/tex]Like the first question, let's find some factors7[tex]\sqrt[]{4 * 6}[/tex] + [tex]\sqrt[]{9 * 10}[/tex] - 8[tex]\sqrt[]{9 * 6}[/tex]Aha! Looks like we found a couple more squares!7[tex]\sqrt[]{(2*2) * 6}[/tex] + [tex]\sqrt[]{(3*3) * 10}[/tex] - 8[tex]\sqrt[]{(3*3) * 6}[/tex]Square all of them:7*2[tex]\sqrt[]{6}[/tex] + 3[tex]\sqrt[]{10}[/tex] - 8*3[tex]\sqrt[]{6}[/tex]14[tex]\sqrt[]{6}[/tex] + 3[tex]\sqrt[]{10}[/tex] - 24[tex]\sqrt[]{6}[/tex]Note that you can only add numbers with similar leftover roots, so let's do just that:(14[tex]\sqrt[]{6}[/tex] - 24[tex]\sqrt[]{6}[/tex]) + 3[tex]\sqrt[]{10}[/tex]-10[tex]\sqrt[]{6}[/tex] + 3[tex]\sqrt[]{10}[/tex], Option D.If you have any questions, don't be afraid to ask! Good luck :))-T.B.

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