What should be subtracted from the number e + 1 e - 1 to get a rational number?

Given, e + 1 e - 1 = e 2 - 1 2 = e - 1 If we add - e with e - 1 , then we get, - e + e - 1 = - 1 Here, - 1 is a rational number. Therefore, we must add - e with e + 1 e - 1 to get a rational number.

Locate 2 on the number line by geometric method.

Given, 2 Steps of construction: 1 . First draw a straight line such that O denotes the point 0 . 2 . At O draw a unit square O A B C on number line with each side 1 unit in length. 3 . By Pythagoras theorem, O B = O A 2 + A B 2 = 1 + 1 = 2 . 4 . Using a compass with centre O and radius O B , draw an arc on the right side to 0 intersecting the number line at the point k . Therefore, k represents 2 on the number line.

Locate 3 on the number line by geometric method.

Let O represent 0 on the number line. Let A be a point on the number line such that O A = 1 unit. Draw A B perpendicular to O A at A such that A B = 1 unit. Then O B = A B 2 + A O 2 = 1 2 + 1 2 = 2 Again draw C B perpendicular to O B such that C B = 1 . Then O C = O B 2 + C B 2 = 2 2 + 1 2 = 3 Draw an arc with O as centre and O C as radius, draw an arc cutting the line at D . Therefore, D represents 3 on the number line.

Locate 5 on the number line by geometric method.

Let O represent 0 on the number line. Let A be a point on the number line such that O A = 2 units. Draw A B perpendicular to O A at A such that A B = 1 unit. Then O B = A B 2 + A O 2 = 1 2 + 2 2 = 5 With O as centre and O B as radius draw an arc cutting the line at C . Therefore, C represents 5 on the number line.

Locate 7 on the number line by geometric method.

Let O represent 0 on the number line. Let A be a point on the number line such that O A = 1 unit. Draw A B perpendicular to O A at A such that A B = 1 unit. Then O B = A B 2 + A O 2 = 1 2 + 1 2 = 2 With O as centre and O B as radius draw an arc cutting the line at C . Then O C = O B = 2 Again draw C D perpendicular to the line such that C D = 1 . Then O D = O C 2 + C D 2 = 2 2 + 1 2 = 3 Draw an arc with O as centre and O D as radius, draw an arc cutting the line at E . Then O E = O D = 3 Draw E F perpendicular to the number line at E such that E F = 2 and join O F . Now, O F = O E 2 + E F 2 = 3 2 + 2 2 = 7 With O as centre and O F as radius, draw an arc cutting the line at G . Therefore, G represents 7 on the number line.

Represent the numbers - 18 , - 17 , 17 and 18 on the same number line.

Given, - 18 , - 17 , 17 and 18 Let O represent 0 on the number line. Let A be a point on the number line such that O A = 3 units. Draw A B perpendicular to O A at A such that A B = 3 units. Then O B = A B 2 + A O 2 = 3 2 + 3 2 = 18 With O as centre and O B as radius draw an arc cutting the line at F . Thus, F represents 18 on the number line. Again, with O as centre and O B as radius draw an arc to the left of O cutting the line at Q . Thus, Q represents - 18 on the number line. Let C be a point on the line such that O C = 4 units. Again draw C D perpendicular to the line such that C D = 1 . Then O D = O C 2 + C D 2 = 4 2 + 1 2 = 17 Draw an arc with O as centre and O D as radius, draw an arc to the right of O cutting the line at E . Thus, E represents 17 on the number line. Again, with O as centre and O D as radius, draw an arc to the left of O cutting the line at P . Therefore, P represents - 17 on the number line.