Question

(2) Prove that 3 + square root 15 is an irrational number.
(3) Represent the numbers square root 15 and square root 10 on a number line.
please show that step by step please​

Answer 1

Answer:

3)to represent root 15 we use pythagoras theorem

in a right angled triangle we will take base as 1 and hypotenuse as 4  

thus the perpendicular root will be 15..

to draw the root 15,draw a line BC =1 unit draw BA perpendicular to BC.

from C cut an arc of length 4 units,let it itersect at the perpendicular at A.

Thus AB =root 15..

Step-by-step explanation:

Let us assume that 3 + √5 is a rational number.

Now,

3 + √5 = (a ÷ b)

[Here a and b are co-prime numbers]

√5 = [(a ÷ b) - 3]

√5 = [(a - 3b) ÷ b]

Here, {(a - 3b) ÷ b} is a rational number.

But we know that √5 is a irrational number.

So, {(a - 3b) ÷ b} is also a irrational number.

So, our assumption is wrong.

3 + √5 is a irrational number.