Question

with explaination ?​

Answer 1

1)

$2 - \sqrt{5}$

value of root 5 is 2.23....

2-2.23...

0.23...

the answer is non terminatimg and non repeating.

So it is irrational.

2)

$(3 + \sqrt{23} ) - \sqrt{23} \\ 3 + \sqrt{23} - \sqrt{23} \\ = 3$

the answer is 3. so it is irrational.

3)

$\frac{2 \sqrt{11} }{7 \sqrt{11} } \\ = \frac{2}{7}$

root 11 will cancel out.

the answer is rational.

4)

$\frac{1}{ \sqrt{3} }$

$\sqrt{3} = 1.73....$

root 3 is irrational so, it is irrational.

5)

$5\pi \\ \pi = 3.14.... \\ 5 \times 3.14...$

pi is irrational so, 5pi is also irrational

Answer 2

I) is irrational

2)

$(3 + \sqrt{23} ) - \sqrt{23}$

is irrational because root 23 is irrational

3)is rational

4)irrational

5)irrational, because pi is irrational

when we convert the picture into decimal form we will get non terminating not recuring decimal expansion