Question

1. 2 radical 3+7 radical 3-6 radical 3=
2.5radical 5 -10 radical 5+ radical 5=
3. 7 radical -2 radical 2 -5 radical 2- radical 2=
4.2 radical 5+3 radical -5 radical 5=
5. 3 radical 2+2 radical 3 -radical 3 + radical 2=
6. 2 radical 5-3 radical 3 +radical 5+7 radical 3 + radical 5=
7 7 radical 2-8 radical 2 +3+5 radical 3 - radical 3=
8. 2 radical 5+3 radical 2-4+5 radical 3 - radical 3=

Answer 1

1)  2√3 + 7√3 - 6√3 = 9√3 - 6√3 = 3√3

2)  5√5 - 10√5 + √5 = - 5√5 +√5 = - 4√5

3)   7√2 - 2√2 - 5√2 - √2 = - √2

4).  2√5 + 3√5 - 5√5 = 5√5 - 5√5 = 0

5)  3√2 + 2√3 - √3 + √2 = ( 3√2 + √2 ) + ( 2√3 - √3 ) = 4√2 + √3

6)  2√5 - 3√3 + √5 + 7√3 + √5 = 4√5 + 4√3 = 4 ( √5 + √3 )

7)  7√2 - 8√2 + 3 + 5√3 - √3 = 3 - √2 + 4√3

8) 2√5 + 3√2 - 4 + 5√3 - √3 = 2√5 + 3√2 + 4√3 - 4

Answer 2

$a)2 \sqrt{3} + 7 \sqrt{3} - 6 \sqrt{3} = (2 + 7 - 6) \sqrt{3} = 3 \sqrt{3}$

$b)5 \sqrt{5} - 10 \sqrt{5} + \sqrt{5} = 5 \sqrt{5} - 10 \sqrt{5} + 1 \sqrt{5} = (5 - 10 + 1) \sqrt{5} = - 4 \sqrt{5}$

$c)7 \sqrt{2} - 2 \sqrt{2} - 5 \sqrt{2} - \sqrt{2} = 7 \sqrt{2} - 5 \sqrt{2} - 2 \sqrt{2} - 1 \sqrt{2} = (7 - 5 - 2 - 1) \sqrt{2} = - 1 \sqrt{2} = - \sqrt{2}$

$d)2 \sqrt{5} + 3 \sqrt{5} - 5 \sqrt{5} = (2 + 3 - 5) \sqrt{5} = 0 \sqrt{5} = \sqrt{5}$

$e)3 \sqrt{2} + 2 \sqrt{3} - \sqrt{3} + \sqrt{2} = (3 \sqrt{2} + \sqrt{2} ) + (2 \sqrt{3} - \sqrt{3}) = 4 \sqrt{2} + \sqrt{3}$

$f)2 \sqrt{5} - 3 \sqrt{3} + \sqrt{5} + 7 \sqrt{3} + \sqrt{5} = (2 \sqrt{5} + \sqrt{5} + \sqrt{5}) + ( - 3 \sqrt{3} + 7 \sqrt{3}) = 4 \sqrt{5} + 4 \sqrt{3}$

$g)7 \sqrt{2} - 8 \sqrt{2} + 3 + 5 \sqrt{3} - \sqrt{3} = (7 \sqrt{2} - 8 \sqrt{2}) + 3 + (5 \sqrt{3} - \sqrt{3}) = - \sqrt{2} + 3 + 4 \sqrt{3}$

$h)2 \sqrt{5} + 3 \sqrt{2} - 4 + 5 \sqrt{3} - \sqrt{3} = 2 \sqrt{5} + 3 \sqrt{2} - 4 + (5 \sqrt{3} - \sqrt{3} ) = 2 \sqrt{5} + 3 \sqrt{2} - 4 + 4 \sqrt{3}$