Represent 7–√ on the number line.

Hint: Use the fact that if two sides of a right-angled triangle are x−−√ and 1, then the hypotenuse is given by x+1−−−−−√. Hence form a right-angled triangle with sides, 1 and 1. The hypotenuse will be 2–√. Then using the length of hypotenuse form another right-angled triangle with sides, 3–√ and 1. The hypotenuse of that triangle will be 3–√. Continue in the same way till we get the hypotenuse length as 7–√. Now extend compass length to be equal to 7–√ (Keep one arm of the compass on one endpoint of the hypotenuse and the other arm on the other endpoint of the hypotenuse). Draw an arc with 0 as the centre and let it intersect the positive x-axis at some point. The point then represents 7–√ on the number line. Complete step-by-step answer: Consider a right-angled triangle with side length as 1,1 as shown below Hence BC=12+12−−−−−−√=2–√ Draw CD perpendicular BC and CD = 1 unit as shown below. Hence BD=(2–√)2+12−−−−−−−−−√=3–√ Draw CE perpendicular to BD, CE = 1 unit. Hence BE=(3–√)2+1−−−−−−−−√=4–√ Draw EF perpendicular to BE, EF = 1 unit as shown below Hence BF=(4–√)2+1−−−−−−−−√=5–√ Draw FG perpendicular BF and FG = 1 unit as shown below. Hence BG=(5–√)2+1−−−−−−−−√=6–√ Draw GH perpendicular BG and GH = 1 unit, as shown below. Hence BH=(6–√)2+1−−−−−−−−√=7–√ With O as centre and radius BH, mark draw an arc and let it intersect the positive x-axis at M. M represents 7–√ on the number line. Hence 7–√ is represented on the number line. Note: Alternative method: Best Method: Draw OX = 7 units. Extend OX to P such that XP = 1 unit. Now locate the midpoint of OP by drawing perpendicular bisector of OP. Let it intersect OP at A as shown below. With A as centre and radius OP draw a semicircle as shown below Now draw a line parallel to the perpendicular bisector through X and let it intersect the semicircle at B as shown below. Hence XB=7–√ Now extend compass to be of radius XB draw an arc from O and let it intersect OP at C. C represents 7–√ on the number line.