Name: Multiplying Irrational Numbers
Uploaded: 2019-07-19
Duration: 1 min 13 s
Description: On multiplying two irrational numbers, what will you get? A rational number or maybe an irrational number? Let us find out the answer in this video.

Question

Locate

\sqrt{7}

on the number line by geometric method.

Accepted Answer

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 $O B = \sqrt{A B^{2} + A O^{2}} = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$

With $O$ as centre and $O B$ as radius draw an arc cutting the line at $C$ .

Then $O C = O B = \sqrt{2}$

Again draw $C D$ perpendicular to the line such that $C D = 1$ .

Then $O D = \sqrt{O C^{2} + C D^{2}} = \sqrt{{(\sqrt{2})}^{2} + 1^{2}} = \sqrt{3}$

Draw an arc with $O$ as centre and $\sqrt{7}$ as radius, draw an arc cutting the line at $E$ .

Then $O E = O D = \sqrt{3}$

Draw $E F$ perpendicular to the number line at $E$ such that $E F = 2$ and join $O F$ .

Now, $O F = \sqrt{O E^{2} + E F^{2}} = \sqrt{{(\sqrt{3})}^{2} + 2^{2}} = \sqrt{7}$

With $O$ as centre and $O F$ as radius, draw an arc cutting the line at $G$ .

Therefore, $G$ represents $\sqrt{7}$ on the number line.

Locate $\sqrt{7}$ on the number line by geometric method.

Important Questions on Real Numbers

Learn and Prepare for any exam you want !

Locate 7 on the number line by geometric method.

Important Questions on Real Numbers

Learn and Prepare for any exam you want !

Locate $\sqrt{7}$ on the number line by geometric method.