Question

3.
Show how root 5 can be represent in the number line​

Answer 1

Answer:

Hint: We denote the points representing 0 and 2 in the number line as O and A. We construct a right angled triangle OAB such that ∠OAB is the right angle and AB=1 unit. We use the Pythagoras theorem and find OB=5–√ units. We take an arc OB from the point of O and cut the number line at the point G. G represents 5–√ in the number line.

Complete step-by-step answer:

We know from Pythagora's theorem states that “In a right-angled triangle the square of hypotenuse is sum of squares of other two sides.” If h is the length of hypotenuse and p,b are the lengths of other two sides, then we have

h2=p2+b2

If we can find a length of 5–√ and take an arc of that length from point 0 in the number line we can show the position of 5–√. Let us choose the hypotenuse as h=5–√. So we haveh2=(5–√)2=5. We can choose two perfect squares p2=4,b2=1 such thatp2+b2=h2=5. Then we have p=2,b=1.

We denote the point representing 0 and 2 in the number line as O and A. The line segment OA will be our choice for p=2.We draw the right angle at the point of A and construct the right angle triangle ΔOAB such that AB=1unit. The line segment OB will be our choice for p=1.

We see that in the above right angled triangle OAB is the hypotenuse h=OB. So by Pythagoras theorem we have,

OB2=OA2+AB2⇒h2=p2+b2⇒h=p2+b2−−−−−−√⇒h=22+12−−−−−−√=5–√

We take the arc OB=5–√ from O and cut the number line at the point G. G will represent the number 5–√ in the number line.

Note: We note that 5–√ is an irrational number which means 5–√ cannot be expressed in the form of pqwhere p is any integer and q is a non-zero integer. We can alternative solve by choosing p2=2,b2=3 but or that we need to construct right angled triangles with hypotenuse of length 2–√,3–√units.

69.3K+ Views

Answer 2

Answer:

this is your answer..

hope it helps

Step-by-step explanation:

please it is a request please mark me brainliest

have a nice day..

bye bye