Question

Please help as soon as possible ​

Answer 1

Answer:

I

1) given here

(3+√2)/(3-√2)=m+n√2.

=>(3+√2)(3+√2)/(3+√2)(3-√2)=m+n√2.

=>(9+2+4√2)/9-2=m+n√2

=>(11+4√2)/7=m+n√2

=>11/7+4√2/7=m+n√

compare. both side

m=11/7,

and ,

n=4/7.

2) a)  x = 5 - 2√6

1/x = {1/(5 - 2√6)

⇒ 1/x = {1/(5 - 2√6)} × (5 + 2√6)/(5 + 2√6)

= (5 + 2√6)/25 - 24

= 5 + 2√6

Now,

(√x + 1/√x²) = x + 1/x + 2 × √x × 1/√x

= x + 1/x + 2

⇒ √x + 1/√x = √x + 1/x + 2 (whole root)

= √5 - 2√6 + 5 + 2√6 + 2

= √5 + 5 + 2

= √12

b) x=5-2√6

Then 1/x=5+2√6. ( by rationalization)

(5-2√6)²+(5+2√6)²

25+24-20√6+ 25+ 24+20√6

25+24+25+24

50+48

98 is your answer

3) let us assume 2+√3 as rational.

⇒2+√3=a/b

∴2-a/b=-√3 or √3=a/b-2

⇒√3=a/b-2

√3=a-2b/b

∵a and b are positive integers  

∴a-2b/b is rational

⇒√3 is rational

but we know that √3 is irrational

∴⇒2+√3 is irrational

4) the given numbers are 5 and 6

the rational no. (by mean or average method we get)

5+6/2 = 11/2

the irrational no. 5.1313113111311113....

6) √24=4.89897948......

∛35=2.43229927.......

∴ 4.89... > 2.43...

∴√24 > ∛35

Step-by-step explanation: