Question

let me place root 5 on number line

Answer 1

Step-by-step explanation:

$There are two ways.$

$First one. \\ \\ Let 5, the square of \ \sqrt{5},\ be written as sum of two squares. \\ \\ The following is such possible one. \\ \\ \\ 5 = 1 + 4 = 1^2 + 2^2 \\ \\ \\ So we're going to place \sqrt{5}\ on number line by this.$

$1.  \ Mark point O at 0. \\ \\ 2. \ Mark point A at 1. \\ \\ 3. \ Draw a 2 unit long line segment perpendicular to the number line at point A. Mark the top end of this segment as B. \\ \\ 4. \ Join OB. \\ \\ 5. \ Draw an arc of radius OB with center O so that the arc should meet the number line on the right side. Mark this point as C. \\ \\ \\ \therefore\ C is \ \sqrt{5}.$

$Second one. \\ \\ Let 5 be written as difference of two squares. \\ \\ The following is such possible one. \\ \\ \\ 5 = 9 - 4 = 3^2 - 2^2 \\ \\ \\ So we're going to place \ \sqrt{5}\ on number line by this.$

$1. \ Mark point O at 0. \\ \\ 2. \ Mark point A at \ -2. \\ \\ 3. \ Draw a line perpendicular to the number line at O. \\ \\ 4. \ Draw an arc of radius 3 units with center A so that the arc should cut the line perpendicular to the number line at O. \\ \\ 5. \ Mark this point, where the arc cuts the line, as B. Join AB if needed. \\ \\ 6. \ Draw another arc of radius OB with center O so that the arc should meet the number line on the right side. Mark this point as C. \\ \\ \\ \therefore\ C is \ \sqrt{5}.$

$The responsible figures are also attached with this.$

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