Question

Express 1.6666... as a rational number in the form of p/q.

Name an irrational number between Root 2 and Root 3.

Find the rationalising factor of Root 5 + Root 3


ANSWER WITH METHOD PLEASE!

Answer 1

1.) 1.6bar =p/q (1)
multiple by 10both sudes
10 p/q = 16.6 bar (2)
p/q = 1.6 bar. (1)
9p/q = 15
p/q = 15/9

Answer 2

Answer and Explanation :

1) Given : Number 1.666..

To find : Express number as a rational number in the form of p/q ?

Solution :

Let $x=1.6666$ ....(1)

Multiply both side by 10,

$10x=16.666...$ .....(2)

Subtract (1) and (2),

$10x-x=(16.666...)-(1.6666)$

$9x=15$

$x=\frac{15}{9}$

$x=\frac{5}{3}$

2) Given : Number $\sqrt{2}$ and  $\sqrt{3}$

To find : Name an irrational number between numbers?

Solution :

Irrational number cannot be written in simplest fraction form or p/q for.

Irrational numbers area non-terminating and non-repeating.

$\sqrt{2}=1.41421356237..$

$\sqrt{3}=1.73205080757..$

Irrational number between therm is 1.5648634258....

3) Given : Expression $\sqrt{5}+\sqrt{3}$

To find : The rationalizing factor of the expression?

Solution :

The rationalizing factor is defined as the factor of multiplication by which rationalization is done or the conjugate of the factor.

The conjugate of the expression is $\sqrt{5}-\sqrt{3}$

Therefore, The rationalizing factor of the given expression is $\sqrt{5}-\sqrt{3}$