Question

pls answdr all the questions fast

Answer 1

1) (1^0 + 2 ^0 + 3^0) ² = (1+1+1)² = 3² = 9 (a^0 = 1)

2) a^a + b^b = 3³ + 5^5 = 27 + 3125 =3152

3)✓3+√5/✓5-✓3 + ✓5 -✓3/✓5+✓3
= (✓3+✓5)² + (✓5-✓3)²/(✓5-✓3)(✓5+✓3)
= 3+5+2✓15+3+5-2✓15/5-3
=8+8/2
=16/2
=8

4) a - 1/a = a²-1/a
Putting value of a
(3+✓8)²-1/3+✓8
= 9+8+6✓8 -1/3+✓8
=16+6✓8/3+✓8
Rationalising the denominator-
16+6✓8/3+✓8 × 3-✓8/3-✓8
= 16+6✓8(3-✓8)/3²-(✓8)²
=48-16✓8+18✓8-48/9-8
=2✓8/1
=2✓8

5)Let x be 0.235235.....
then, 100x = 235.235235....
– x = 0.235235....
____________________
99x = 235
or, x = 235/99

6) Let's multiply 1 and 2 by 10/10
=> 1/1×10/10 and 2/1×10/10
or , 10/10 and 20/10
5 nos between 10/10 and 20/10 are -
11/10 , 12/10 , 13/10 , 14/10 , 15/10

7)First five positive numbers whose sq. root is irrational are -
2 , 3 , 5 , 6 and 7

9) x² + 1/x² = (4-✓15)²- 1/(4-✓15)²
= 16-15 - 1/ (16-15)
= 1 - 1/1 = 1-1 = 0

12) Remainder is 3.