1.
Blanks
1. The number whose square root is the number itself is _______
2 are _______; the principal square root of 2 is
2 2
2. The square roots of
______.
3. The square roots of the reciprocal of the absolute value of 256 are ________.
4. The integer part of 7 is _______and its decimal part is _______.
5. The integer part of 21 1 is _______and its decimal part is _______.
6. Given 10404 102 and x 0.102 . Then x equals _______.
7. Find the values of x such that 2 x 1 has no square root.___________
8. Find the values of x such that x x is defined.___________
9. Compare 8 ____ 10 and 3 2 ____ 2 5
10. How many positive integers less than 5 5 ?
11. If the square of a number is a, then the number is the ______ of a;
12. A positive number has ____square root(s), whose sum is ______; the square root
of 0 is _______; ________numbers have no square roots.
13. The square roots of 4 are ______ and the square roots of 0.25 are ______.
14. The principal square root of 121 is _____ and the negative square root of 169 is_.
15. 4 is the square root of ______ and 0.01 is the square root of _______.
16. 256 _____ , 16 _____ and 196 _____
17. Given x 3 , then x ____ ; Given x 2 3 , then x ____ .
2
1
18. If x 2 , then x ____ .
7
19. The square of 81 is and the square roots of 81 are ______ .
2. Multiple-choices
1. Choose the right one
A. Any number has two square roots C. Only positive number has square roots
B. The square of the square roots of a positive number is the number itself
D. A number has no square root except a positive number.
2. Which is undefined?
3
2
A. 32 B. 32 C. D. 32
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3. Choose the right one
A. 36 6 B. The square roots of 16 are 4
C. a 2 a D. 7 2 7
a 2
2
4. Given a 2 2 , then the square roots of are
A. 16 B. 16 C. 4 D. 2
5. Given that 4m 1 is defined, then the smallest integer of m is ______.
A. 0 B. 1 C. 1 D. 4
6. Which of the following is a correct description of the statement” the square roots of
81 is ±9”?
A. 81 9 B. 81 9 C. 81 9 D. 81 9
7. Which of the following numbers has a square root?
B. 2 D. 2
2 3
A. 2 C. 2
8. The number of correct ones is
①3 is a square root of 9②the square root of 9 is 3③4 is a positive square root of 8
④ 8 is the negative square root of 64.
A. 1 B. 2 C. 3 D. 4
9. The incorrect one is
A. A positive number has two square roots B. If b 0 , then b has no square root.
C. 6
2
has no square root. D. The square root of a 2 is a .
10. Among the positive square root of integers from 1 to 10, how many roots are
rational numbers?
B. 1 B. 2 C. 3 D. 4
3. Calculators:
1. Calculate the radicals to 2 decimal places:
1 3 2 24
5
3 35 4 3
13
5 0.03581 6 5280
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2. Given that 3m 2 and 3m 2 are square roots of a number, find the values of m
and the number.
3. Given that the square roots of a number are 3m 2 and 3m 2 , find the values
of m and the number.
a 3 b 5 0 , find the square roots of a b
2 2
4. Given .
5. Given x 2 y 1 0 , find x y .
6. Given 9 y 2 16 0 and y is positive, find the principal square root of 3 y 5 .
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