Revision Exercise on Quadratic Radicals
1. Fill in the blanks:
(a) When
x _______,
(b) When a  3 ,
1 3x is meaningful.
15  a 2  _________.
(c) Given x  3  2 , y  3  2 , then x 3 y  xy3  _____________.
(d) Compare:  3 2 ______  2 3
(e) (√3 − 2)
2000
2𝑏
⋅ (√3 + 2)
2001
= ______________
𝑎
(f) Simplify: √ 𝑎 ⋅ √18𝑏 =_________;
(g) Given that
3  x2
(h) Given that
4a  3b and
25  24  _________;
2
2
16b 2 c
 __________.
a2
 x  3 , the range of values of x is _____________.
b 1
2a  b  6 are most simplified quadratic radicals, if they are similar quadratic radicals,
then a  ________, b  ________.
(i) If 3a  1 and a  5 are the two square roots of a real number, then a  ________, the real number is _________.
2. Calculate and simplify:
(b) 4 5  45  8  4 2
2 3 2
(a)


(d) 5 48  6 27  4 15  3


 
(e)

(g) 7  4 3 7  4 3  3 5  1
2
(h)
(c) 6  2
2
1
 18  4
2
2 1
 12 
2 6
 12 
2 6

3
3
3
2
2
(f)
0.01 81
0.25 144
(i)
1
3 2  
2
2
x  3y  x2  9
3. Given
x  3
2
 0 , find the value of
x 1
.
y 1
4. Given a 
1
1
 1  10 , find the value of a 2  2 .
a
a
5. Given x 
20  4
1
2
, find the value of x  2 .
2
x