Opening
\nThe numbers in each column are related. Your goal is to determine how they are related, determine which numbers belong in the blank parts of the columns, and write an explanation for how you know the numbers belong there.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-7-Lesson-3-Example-Answer-Key-1.png\")
\nAnswer:
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-7-Lesson-3-Example-Answer-Key-2.png\")
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-7-Lesson-3-Example-Answer-Key-3.png\")
<\/p>\n
Exercises
\nFind the positive value of x that makes each equation true. Check your solution.<\/p>\n
Exercise 1. b. Solve the equation, and check your answer. Check: Exercise 2. Check: Exercise 3. Check: Exercise 4. Check: Exercise 5. Check: Exercise 6. Exercise 7. Check: Exercise 8. Check: Exercise 9. Find the positive value of x that makes each equation true. Check your solution. Check: Question 2. Check: Question 3. Check: Question 4. Check: Question 5. b. Solve and check your solution. Check: Question 6. Check: Question 7. Check: Question 8. Check: Question 9. Find the positive value of x that makes each equation true. Check your solution. b. Solve and check your solution. Check: Question 2. Check: Question 3. Check: Question 4. Check: Engage NY Eureka Math 8th Grade Module 7 Lesson 3 Answer Key Eureka Math Grade 8 Module 7 Lesson 3 Exercise Answer Key Opening The numbers in each column are related. Your goal is to determine how they are related, determine which numbers belong in the blank parts of the columns, and write an explanation … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/82176"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=82176"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/82176\/revisions"}],"predecessor-version":[{"id":137305,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/82176\/revisions\/137305"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=82176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=82176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=82176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nx2<\/sup> = 169
\na. Explain the first step in solving this equation.
\nAnswer:
\nThe first step is to take the square root of both sides of the equation.<\/p>\n
\nAnswer:
\nx2<\/sup> = 169
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{169}\\)
\nx = \\(\\sqrt{169}\\)
\nx = 13<\/p>\n
\n132<\/sup> = 169
\n169 = 169<\/p>\n
\nA square-shaped park has an area of 324 yd2<\/sup>. What are the dimensions of the park? Write and solve an equation.
\nx2<\/sup> = 324
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{324}\\)
\nx = \\(\\sqrt{324}\\)
\nx = 18<\/p>\n
\n182<\/sup> = 324
\n324 = 324
\nThe square park is 18 yd. in length and 18 yd. in width.<\/p>\n
\n625 = x2<\/sup>
\n625 = x2<\/sup>
\n\\(\\sqrt{625}\\) = \\(\\sqrt{x^{2}}\\)
\n\\(\\sqrt{625}\\) = x
\n25 = x<\/p>\n
\n625 = 252<\/sup>
\n625 = 625<\/p>\n
\nA cube has a volume of 27 in3<\/sup>. What is the measure of one of its sides? Write and solve an equation.
\n27 = x3<\/sup>
\n\\(\\sqrt [ 3 ]{ 27 }\\) = \\(\\sqrt[3]{x^{3}}\\)
\n\\(\\sqrt [ 3 ]{ 27 }\\) = x
\n3 = x<\/p>\n
\n27 = 33<\/sup>
\n27 = 27
\nThe cube has side lengths of 3 in.<\/p>\n
\nWhat positive value of x makes the following equation true: x2<\/sup> = 64? Explain.
\nx2<\/sup> = 64
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{64}\\)
\nx = \\(\\sqrt{64}\\)
\nx = 8<\/p>\n
\n82<\/sup> = 64
\n64 = 64
\nTo solve the equation, I need to find the positive value of x so that when it is squared, it is equal to 64. Therefore, I can take the square root of both sides of the equation. The square root of x2<\/sup>, \\(\\sqrt{52}\\), is x because x2<\/sup> = x \u2219 x. The square root of 64, \\(\\sqrt{64}\\), is 8 because 64 = 8 \u2219 8. Therefore, x = 8.<\/p>\n
\nWhat positive value of x makes the following equation true: x3<\/sup> = 64? Explain.
\nAnswer:
\nx3<\/sup> = 64
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt [ 3 ]{ 64 }\\)
\nx = \\(\\sqrt [ 3 ]{ 64 }\\)
\nx = 4 Check:
\n43<\/sup> = 64
\n64 = 64
\nTo solve the equation, I need to find the positive value of x so that when it is cubed, it is equal to 64. Therefore, I can take the cube root of both sides of the equation. The cube root of x3<\/sup>, \\(\\sqrt[3]{x^{3}}\\), is x because x3<\/sup> = x \u2219 x \u2219 x. The cube root of 64, \\(\\sqrt [ 3 ]{ 64 }\\), is 4 because 64 = 4 \u2219 4 \u2219 4. Therefore, x = 4.<\/p>\n
\nFind the positive value of x that makes the equation true: x2<\/sup> = 256-1<\/sup>.
\nAnswer:
\nx2<\/sup> = 256-1<\/sup>
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{256^{-1}}\\)
\nx = \\(\\sqrt{256^{-1}}\\)
\nx = \\(\\sqrt{\\frac{1}{256}}\\)
\nx = \\(\\frac{1}{16}\\)
\nx = 16-1<\/sup><\/p>\n
\n(16-1<\/sup>)2<\/sup> = 256-1<\/sup>
\n16-2<\/sup> = 256-1<\/sup>
\n\\(\\frac{1}{16^{2}}\\) = 256-1<\/sup>
\n\\(\\frac{1}{256}\\) = 256-1<\/sup>
\n256-1<\/sup> = 256-1<\/sup><\/p>\n
\nFind the positive value of x that makes the equation true: x3<\/sup> = 343-1<\/sup>.
\nx3<\/sup> = 343-1<\/sup>
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt[3]{343^{-1}}\\)
\nx = \\(\\sqrt[3]{343^{-1}}\\)
\nx = \\(\\sqrt[3]{\\frac{1}{343}}\\)
\nx = \\(\\frac{1}{7}\\)
\nx = 7-1<\/sup><\/p>\n
\n(7-1<\/sup>)3<\/sup> = 343-1<\/sup>
\n73<\/sup>\u00a0= 343-1<\/sup>
\n(\\(\\frac{1}{7}\\))3<\/sup> = 343-1<\/sup>
\n\\(\\frac{1}{343}\\) = 343-1<\/sup>
\n343-1<\/sup> = 343-1<\/sup><\/p>\n
\nIs 6 a solution to the equation x2 <\/sup>– 4 = 5x? Explain why or why not.
\nAnswer:
\n62 <\/sup>– 4 = 5(6)
\n36 – 4 = 30
\n32 \u2260 30
\nNo, 6 is not a solution to the equation x2 <\/sup>– 4 = 5x. When the number is substituted into the equation and simplified, the left side of the equation and the right side of the equation are not equal; in other words, it is not a true number sentence. Since the number 6 does not satisfy the equation, it is not a solution to the equation.<\/p>\nEureka Math Grade 8 Module 7 Lesson 3 Problem Set Answer Key<\/h3>\n
\nQuestion 1.
\nWhat positive value of x makes the following equation true: x2<\/sup> = 289? Explain.
\nAnswer:
\nx2<\/sup> = 289
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{289}\\)
\nx = \\(\\sqrt{289}\\)
\nx = 17<\/p>\n
\n172<\/sup> = 289
\n289 = 289
\nTo solve the equation, I need to find the positive value of x so that when it is squared, it is equal to 289. Therefore, I can take the square root of both sides of the equation. The square root of x2<\/sup>, \\(\\sqrt{x^{2}}\\), is x because x2<\/sup> = x \u22c5 x. The square root of 289, \\(\\sqrt{289}\\) , is 17 because 289 = 17 \u22c5 17. Therefore, x = 17.<\/p>\n
\nA square-shaped park has an area of 400 yd2<\/sup>. What are the dimensions of the park? Write and solve an equation.
\nAnswer:
\nx2<\/sup> = 400
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{400}\\)
\nx = \\(\\sqrt{400}\\)
\nx = 20<\/p>\n
\n202<\/sup> = 400
\n400 = 400
\nThe square park is 20 yd. in length and 20 yd. in width.<\/p>\n
\nA cube has a volume of 64 in3<\/sup>. What is the measure of one of its sides? Write and solve an equation.
\nAnswer:
\nx3<\/sup> = 64
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt [ 3 ]{ 64 }\\)
\nx = \\(\\sqrt [ 3 ]{ 64 }\\)
\nx = 4<\/p>\n
\n43<\/sup> = 64
\n64 = 64
\nThe cube has a side length of 4 in.<\/p>\n
\nWhat positive value of x makes the following equation true: 125 = x3<\/sup>? Explain.
\nAnswer:
\n125 = x3<\/sup>
\n\\(\\sqrt [ 3 ]{ 125 }\\) = \\(\\sqrt[3]{x^{3}}\\)
\n\\(\\sqrt [ 3 ]{ 125 }\\) = x
\n5 = x<\/p>\n
\n125 = 53<\/sup>
\n125 = 125
\nTo solve the equation, I need to find the positive value of x so that when it is cubed, it is equal to 125. Therefore, I can take the cube root of both sides of the equation. The cube root of x3<\/sup>, \\(\\sqrt[3]{x^{3}}\\), is x because x3<\/sup> = x \u22c5 x \u22c5 x. The cube root of 125, \\(\\sqrt [ 3 ]{ 125 }\\), is 5 because 125 = 5 \u22c5 5 \u22c5 5. Therefore, x = 5.<\/p>\n
\nFind the positive value of x that makes the equation true: x2<\/sup> = 441-1<\/sup>.
\na. Explain the first step in solving this equation.
\nAnswer:
\nThe first step is to take the square root of both sides of the equation.<\/p>\n
\nx2<\/sup> = 441-1<\/sup>
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{144^{-1}}\\)
\nx = \\(\\sqrt{144^{-1}}\\)
\nx = \\(\\sqrt{\\frac{1}{441}}\\)
\nx = \\(\\frac{1}{21}\\)
\nx = 21-1<\/sup><\/p>\n
\n(21-1<\/sup> )2<\/sup> = 441-1<\/sup>
\n21-2<\/sup> = 441-1<\/sup>
\n\\(\\frac{1}{21^{2}}\\) = 441-1<\/sup>
\n\\(\\frac{1}{441}\\) = 441-1<\/sup>
\n441-1<\/sup> = 441-1<\/sup><\/p>\n
\nFind the positive value of x that makes the equation true: x3<\/sup> = 125-1<\/sup>.
\nAnswer:
\nx3<\/sup> = 125-1<\/sup>
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt[3]{125^{-1}}\\)
\nx = \\(\\sqrt[3]{125^{-1}}\\)
\nx = \\(\\sqrt[3]{\\frac{1}{125}}\\)
\nx = \\(\\frac{1}{5}\\)
\nx = 5-1<\/sup><\/p>\n
\n(5-1<\/sup>)3<\/sup> = 125-1<\/sup>
\n5-3<\/sup> = 125-1<\/sup>
\n\\(\\frac{1}{5^{3}}\\) = 125-1<\/sup>
\n\\(\\frac{1}{125}\\) = 125-1<\/sup>
\n125-1<\/sup> = 125-1<\/sup><\/p>\n
\nThe area of a square is 196 in2<\/sup>. What is the length of one side of the square? Write and solve an equation, and then check your solution.
\nAnswer:
\nLet x in. represent the length of one side of the square.
\nx2<\/sup> = 196
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{196}\\)
\nx = \\(\\sqrt{196}\\)
\nx = 14<\/p>\n
\n142<\/sup> = 196
\n196 = 196
\nThe length of one side of the square is 14 in.<\/p>\n
\nThe volume of a cube is 729 cm3<\/sup>. What is the length of one side of the cube? Write and solve an equation, and then check your solution.
\nAnswer:
\nLet x cm represent the length of one side of the cube.
\nx3<\/sup> = 729
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt [ 3 ]{ 729 }\\)
\nx = \\(\\sqrt [ 3 ]{ 729 }\\)
\nx = 9<\/p>\n
\n93<\/sup> = 729
\n729 = 729
\nThe length of one side of the cube is 9 cm.<\/p>\n
\nWhat positive value of x would make the following equation true: 19 + x2<\/sup> = 68?
\nAnswer:
\n19 + x2<\/sup> = 68
\n19 – 19 + x2<\/sup> = 68 – 19
\nx2<\/sup> = 49
\nx = 7
\nThe positive value for x that makes the equation true is 7.<\/p>\nEureka Math Grade 8 Module 7 Lesson 3 Exit Ticket Answer Key<\/h3>\n
\nQuestion 1.
\nx2<\/sup> = 225
\na. Explain the first step in solving this equation.
\nAnswer:
\nThe first step is to take the square root of both sides of the equation.<\/p>\n
\nAnswer:
\nx2<\/sup> = 225
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{225}\\)
\nx = \\(\\sqrt{225}\\)
\nx = 15<\/p>\n
\n152<\/sup> = 225
\n225 = 225<\/p>\n
\nx3<\/sup> = 64
\nAnswer:
\nx3<\/sup> = 64
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt[3]{ 64 }\\)
\nx = \\(\\sqrt [ 3 ]{ 64 }\\)
\nx = 4<\/p>\n
\n43<\/sup> = 64
\n64 = 64<\/p>\n
\nx2<\/sup> = 361-1<\/sup>
\nAnswer:
\nx2<\/sup> = 361-1<\/sup>
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{361^{-1}}\\)
\nx = \\(\\sqrt{361^{-1}}\\)
\nx = \\(\\sqrt{\\frac{1}{361}}\\)
\nx = \\(\\frac{1}{19}\\)
\nx = 19-1<\/sup><\/p>\n
\n(19-1<\/sup>)2<\/sup> = 361-1<\/sup>
\n19-2<\/sup> = 361-1<\/sup>
\n\\(\\frac{1}{19^{2}}\\) = 361-1<\/sup>
\n\\(\\frac{1}{361}\\) = 361-1<\/sup>
\n361-1<\/sup> = 361-1<\/sup><\/p>\n
\nx3<\/sup> = 1000-1<\/sup>
\nAnswer:
\nx3<\/sup> = 1000-1<\/sup>
\n\\(\\sqrt[3]{x^{3}}\\) = \\(\\sqrt[3]{1000^{-1}}\\)
\nx = \\(\\sqrt[3]{1000^{-1}}\\)
\nx = \\(\\sqrt[3]{\\frac{1}{1000}}\\)
\nx = \\(\\frac{1}{10}\\)
\nx = 10-1<\/sup><\/p>\n
\n(10-1<\/sup> )3<\/sup> = 1000-1<\/sup>
\n10-3<\/sup> = 1000-1<\/sup>
\n\\(\\frac{1}{10^{3}}\\) = 1000-1<\/sup>
\n\\(\\frac{1}{1000}\\) = 1000-1<\/sup>
\n1000-1<\/sup> = 1000-1<\/sup><\/p>\n","protected":false},"excerpt":{"rendered":"