Real Numbers

Answer

Step 1: Divide 7 by 16 using long division. Step 2: 7 ÷ 16 = 0.4375 Step 3: Since decimal terminates, it's a terminating decimal. Answer: 0.4375 (terminating decimal, rational number) Why it terminate

Answer

Step 1: Let x = 0.363636... Step 2: Multiply by 100: 100x = 36.363636... Step 3: Subtract: 100x - x = 36.363636... - 0.363636... Step 4: 99x = 36 Step 5: x = 36/99 = 4/11 (simplifying by dividing by 9

Answer

Step 1: First rational = (2/3 + 3/4)/2 = (8/12 + 9/12)/2 = 17/24 Step 2: Second rational = (2/3 + 17/24)/2 = (16/24 + 17/24)/2 = 33/48 = 11/16 Step 3: Third rational = (17/24 + 3/4)/2 = (17/24 + 18/24

Answer

Step 1: Assume √3 is rational, so √3 = p/q where p, q are integers with no common factors. Step 2: Squaring both sides: 3 = p²/q², so p² = 3q² Step 3: This means 3 divides p², so 3 divides p. Let p =

Answer

Step 1: Set up 2.000000 under the radical sign Step 2: Find largest digit whose square ≤ 2: 1² = 1 Step 3: Subtract and bring down: 2 - 1 = 1, bring down 00 → 100 Step 4: Double the quotient (1) = 2,

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Step 1: Draw a number line with O at origin Step 2: Mark unit square OABC with OA = OC = 1 Step 3: By Pythagoras: OB = √(1² + 1²) = √2 Step 4: Draw BD perpendicular to OB with BD = 1 Step 5: By Pythag

Answer

Step 1: Use FOIL method (First, Outer, Inner, Last) Step 2: First: 3 × 2 = 6 Step 3: Outer: 3 × (-√5) = -3√5 Step 4: Inner: √5 × 2 = 2√5 Step 5: Last: √5 × (-√5) = -5 Step 6: Combine: 6 - 3√5 + 2√5 -

Answer

Step 1: Multiply numerator and denominator by conjugate (3 - √2) Step 2: = (1 × (3 - √2))/((3 + √2)(3 - √2)) Step 3: Denominator: (3 + √2)(3 - √2) = 3² - (√2)² = 9 - 2 = 7 Step 4: Numerator: 1 × (3 -