Questions and answers in english

Here are the solutions to your questions in English: 1) Find four rational numbers between 1 and 2. Step 1: To find four rational numbers between 1 and 2, we can express them as fractions with a common denominator. Since we need to find n=4 rational numbers, we multiply the numerator and denominator by (n+1)=5. 1 = (1 × 5)/(5) = (5)/(5) 2 = (2 × 5)/(5) = (10)/(5) Step 2: Now, we can easily find four rational numbers between (5)/(5) and (10)/(5). (6)/(5), (7)/(5), (8)/(5), (9)/(5) Answer: (6)/(5), (7)/(5), (8)/(5), (9)/(5) 2) Find five rational numbers between (3)/(5) and (4)/(5). Step 1: To find five rational numbers between (3)/(5) and (4)/(5), we express them as fractions with a common denominator. Since we need to find n=5 rational numbers, we multiply the numerator and denominator by (n+1)=6. (3)/(5) = (3 × 6)/(5 × 6) = (18)/(30) (4)/(5) = (4 × 6)/(5 × 6) = (24)/(30) Step 2: Now, we can easily find five rational numbers between (18)/(30) and (24)/(30). (19)/(30), (20)/(30), (21)/(30), (22)/(30), (23)/(30) Answer: (19)/(30), (20)/(30), (21)/(30), (22)/(30), (23)/(30) 3) Locate sqrt(3) on the number line. Step 1: Draw a number line. Mark point O at 0 and point A at 1. Step 2: At point A, draw a perpendicular line segment AB of length 1 unit. Step 3: Join O and B. By the Pythagorean theorem, the length of OB is sqrt(OA^2 + AB^2) = sqrt(1^2 + 1^2) = sqrt(2). Step 4: At point B, draw a perpendicular line segment BC of length 1 unit to OB. Step 5: Join O and C. By the Pythagorean theorem, the length of OC is sqrt(OB^2 + BC^2) = sqrt((2))^2 + 1^2 = sqrt(2+1) = sqrt(3). Step 6: With O as the center and OC as the radius, draw an arc that intersects the number line. This intersection point represents sqrt(3). Answer: Follow the steps above to locate sqrt(3) on the number line. That's 2 down. 3 left today — send the next one.