Question

please answer these question please

I will mark it the brain list answer
please answer it please ​

Answer 1

Answer:

Step-by-step explanation:

i)  x=$\frac{1}{2-\sqrt{3} } =\frac{1(2+\sqrt{3} )}{(2-\sqrt{3})(2+\sqrt{3}) } =\frac{2+\sqrt{3} }{2^{2}-\sqrt{3^{2} } } =\frac{2+\sqrt{3} }{4-3} =\frac{2+\sqrt{3} }{1} =2+\sqrt{3}$

ii)   Try doing it by yourself......it is same as the first one

2)

(i) $25^{2} ^{\frac{-1}{4} }=25^{\frac{-1}{2} }$

(ii) try it by yourself

3)

(i)$5^{8}$÷$5^{3} = 5^{8-3} =5^{5} =3125$

(ii)it is very easy you can do it

4) idk

3) let us assume that $\sqrt{3}$ is rational

$\sqrt{3} =\frac{a}{b}$ , a and b are co primes b≠0

$\sqrt{3} b=a$

squaring both sides

3$b^{2}=a^{2}$

3 divides $a^{2}$

⇒3 divides a also----------1

let a=3c

3$b^{2}$=$(3c)^{2}$

3b$^{2} =9c^{2}$

$b^{2} =3c^{2}$

3 divides $c^{2}$

⇒3 divides c also------2

from 1 and 2 we can see that a and b has 3 as it's common factor which is a contradiction to the fact that a and b are co primes

Hence our assumption is wrong

therefore $\sqrt{3}$ is irrational

6),7) sorry I don't know

hope you understand!!!

stay safe!!

pls mark me as brainliest for at least doing this much :)