Question

Represent √7 on number line ​

Answer 1

Answer:

With O as centre and radius BH, mark draw an arc and let it intersect the positive x-axis at M. M represents $\sqrt{7}$ on the number line. Hence $\sqrt{7}$ is represented on the number line.

Answer 2

Hint :-

Use the fact that if two sides of a right-angled triangle are $\sqrt{x}$ and 1, then the

hypotenuse is given by $\sqrt{x+1}$. Hence form a right-angled triangle with sides,

1 and 1. The hypotenuse will be $\sqrt{2}$. Then using the length of hypotenuse form

another right-angled triangle with sides, $\sqrt{2}$ and 1. The hypotenuse of that

triangle will be $\sqrt{3}$. Continue in the same way till we get the hypotenuse

length as $\sqrt{7}$. Now extend compass length to be equal to $\sqrt{7}$ (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 center and let it

intersect the positive x-axis at some point. The point then represents $\sqrt{7}$ on

the number line.

Complete step-by-step answer :-

Consider a right-angled triangle with side length as 1, 1 as shown in fig 1.

Hence BC = $\sqrt{1^2+1^2}$ = $\sqrt{2}$

Draw CD perpendicular to BC and CD = 1 unit as shown in fig 2.

Hence BD = $\sqrt{(\sqrt{2} )^2+1^2}$ = $\sqrt{3}$

Draw CE perpendicular to BD and CE = 1 unit as shown in fig 3.

Hence BE = $\sqrt{(\sqrt{3} )^2+1^2}$ = $\sqrt{4}$

Draw EF perpendicular to BE and EF = 1 unit as shown in fig 4.

Hence BF = $\sqrt{(\sqrt{4} )^2+1^2}$ = $\sqrt{5}$

Draw FG perpendicular BF and FG = 1 unit as shown  in fig 5.

Hence BG = $\sqrt{(\sqrt{5} )^2+1^2}$ = $\sqrt{6}$

Draw GH perpendicular BG and GH = 1 unit as shown in fig 6.

Hence BH = $\sqrt{(\sqrt{6} )^2+1^2}$ = $\sqrt{7}$

With O as center and radius BH,  draw an arc and let it intersect the

positive x-axis at M as shown in fig 7. M represents $\sqrt{7}$ on the number line.

Hence $\sqrt{7}$ is represented on the number line.

Remarks :-

Hope u liked my solution

Pls mark me as brainliest

Thanks.