Question

Represent square roots of 7 and 9 by constructing a square root spiral.

Answer 1

Hint: We will be using the basic concept of Pythagoras theorem and irrational number to solve the problem. Also, we will be using a number line to show the square root spiral.

Complete step-by-step answer:
We have to draw a square root spiral of root 7 and root 9. So, first we will draw for root 7 and then the similar process will be used for root 9.
We will first draw a number line.

Now we will draw a line of 2 units perpendicular on 1 and joint point 0 and the end of the new line.

Now, in $\Delta ABC$we will be applying Pythagoras theorem so we can see that,
$\begin{align}
  & A{{C}^{2}}=B{{C}^{2}}+A{{B}^{2}} \\
 & A{{C}^{2}}=1+4 \\
 & AC=\sqrt{5} \\
\end{align}$
Now we will draw a line of 1 unit perpendicular to AC on A we get $OE=\sqrt{6}$.

Now, again we will be doing the same so we get $OF=\sqrt{7}$.

Similarly for $\sqrt{9}$, we can draw.

Note: These questions are fundamental in nature and required fundamental understanding of the concepts of square root and Pythagoras theorem. It should also be noted that we have to draw the triangles by keeping in mind the square root we have to represent for example for root 7 we have first drawn a triangle having hypotenuse root 5 then again we done the same for making the hypotenuse equal to root 7.