This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To locate sqrt(2) on a number line using the method shown in the image: Step 1: Understand the Pythagorean Theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This is expressed as a^2 + b^2 = c^2. Step 2: Construct a right-angled triangle. Draw a number line and mark the point 0. From 0, measure 1 unit to the right and mark it as point A. At point A (which is at 1 on the number line), draw a perpendicular line segment upwards, also of length 1 unit. Let the endpoint of this segment be B. Step 3: Calculate the length of the hypotenuse. Connect point 0 to point B. This forms a right-angled triangle with legs of length 1 unit each. Using the Pythagorean theorem: c = sqrt(a^2 + b^2) c = sqrt(1^2 + 1^2) c = sqrt(1 + 1) c = sqrt(2) The length of the hypotenuse 0B is sqrt(2) units. Step 4: Transfer the length to the number line. With a compass, place the needle at 0 and open the pencil end to point B. This sets the compass opening to a radius of sqrt(2) units. Draw an arc that intersects the number line to the right of 0. The point where the arc intersects the number line represents the location of sqrt(2). Send me the next one 📸