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Worksheets

quizz 用 by Josie

Total questions: 29

Worksheet time: 18mins

Name
Class
Date
1.

若代数式 5−2xx−1\frac{\sqrt[]{5-2x}}{x-1} 有意义, 则 x 的取值范围是 ( )

a)

x ≤ 5/2 且 x ≠ 1

b)

x < 5/2 且 x ≠ 1

c)

x ≤ 5/2

d)

x < 5/2

2.

若 x, y 都是实数, 且 y = x−4+4−x+9\sqrt[]{x-4}+\sqrt[]{4-x}+9 , 则 y 的平方根是 ( )

a)

6

b)

-6

c)

±√6

d)

±6

3.

二次根式 1x−1\frac{1}{\sqrt[]{x-1}} 中, x 的取值范围是

a)

x ≠ 1

b)

x > 1

c)

x > 1

d)

x₁, 1

4.

已知 a, b 为实数, 且 a = b−8−8−b+25\sqrt[]{b-8}-\sqrt[]{8-b}+25 则 a+b3\sqrt[]{a}+\sqrt[3]{b} 的值为 ( )

a)

-3

b)

9

c)

-3 或 7

d)

7

5.

下列各式中, 不一定是二次根式的是 ( )

a)

√-a (a ≤ 0)

b)

√(a² - 2a + 1)

c)

√(a² + 1)

d)

√(a³)

6.

已知 a, b, c 在数轴上的位置如图所示, 化简 (b−a)2−∣a−c∣−b2\sqrt[]{\left(b-a\right)^2}-\left|a-c\right|-\sqrt[]{b^2} 为

a)

2c

b)

2b - c

c)

2a - 2c

d)

-2a

7.

下列二次根式中, 不是最简二次根式的是 ( )

a)

√(x² - 4)

b)

√(x² + 2x + 4)

c)

√(4x)

d)

√(x² + 4)

8.

Which of the following quadratic radical is the simplest quadratic radical?

a)

√14

b)

13\frac{1}{\sqrt[]{3}}

c)

√8

d)

16\sqrt[]{\frac{1}{6}}

9.

Which of the following quadratic radical is the simplest quadratic radical?

a)

x2+1\sqrt{x^2 + 1}

b)

√27

c)

√0.2

d)

x2y\sqrt{x^2y}

10.

In the following algebraic expressions: π3\sqrt{\frac{\pi}{3}} , 27a\sqrt{27a} , 42\sqrt{42} , 10.7\frac{1}{\sqrt{0.7}} , −(x2−y2)(x+y)-\sqrt{(x^2-y^2)(x+y)} , 523\sqrt[3]{5^2} , x2+y2\sqrt{x^2 + y^2} How many are the simplest quadratic radicals?

a)

0

b)

1

c)

2

d)

3

11.

Among the following expressions: ①√3, ②√(1/4), ③√9, ④√0.5, ⑤√11, how many are the simplest quadratic radicals?

a)

1

b)

2

c)

3

d)

4

12.

Which of the following calculations is incorrect?

a)

√2 × √3 = √6

b)

√8 ÷ √2 = 2

c)

√18 ➗ √2 = 9

d)

(−3)2=3\sqrt[]{\left(-3\right)^2}=3

13.

把 (1−x)1x−1(1-x)\sqrt[]{\frac{1}{x-1}} 根号外面的因式移到根号内得( )

a)

√(1 - x)

b)

√(x - 1)

c)

-√(1 - x)

d)

-√(x - 1)

14.

Calculate √3 × √9, the result is:

a)

3√3

b)

9√3

c)

3

d)

9

15.

Calculate: 67×1321÷236\sqrt[]{7}\times\frac{1}{3}\sqrt[]{21}\div2\sqrt[]{3} . The result is ( )

a)

-4

b)

-2√3

c)

40

d)

7

16.

Which of the following calculations is correct?

a)

√25 = ±5

b)

√-25 = -5

c)

12−1=2+1\frac{1}{\sqrt[]{2-1}}=\sqrt[]{2}+1

d)

12−1=2−1\frac{1}{\sqrt[]{2-1}}=\sqrt[]{2-1}

17.

If a = 2+52+\sqrt[]{5} , b = 12−5\frac{1}{2-\sqrt[]{5}} , then the relationship between a and b is ( )

a)

a > b and they are reciprocals

b)

a > b and they are opposite numbers

c)

ab = -1

d)

ab = 1

18.

25的平方根是( )

a)

-1/√5

b)

-√5

c)

±5

d)

5

19.

Which of the following expressions is the simplest quadratic radical?

a)

0.3\sqrt[]{0.3}

b)

3\sqrt[]{3}

c)

13\sqrt[]{\frac{1}{3}}

d)

13\frac{1}{\sqrt[]{3}}

20.

下列各数中,与 232\sqrt[]{3} 的乘积为有理数的是(  )

a)

√2

b)

√6

c)

√5

d)

333\sqrt[]{3}

21.

Which of the following simplification results is incorrect?

a)

√27 = 3√3

b)

94=32\sqrt[]{\frac{9}{4}}=\frac{3}{2}

c)

23=63\frac{2}{\sqrt[]{3}}=\frac{\sqrt[]{6}}{3}

d)

58=104\sqrt[]{\frac{5}{8}}=\frac{\sqrt[]{10}}{4}

22.

23. 13−5=()\frac{1}{\sqrt{3} - \sqrt{5}} = ( )

a)

3−52\frac{\sqrt{3} - \sqrt{5}}{2}

b)

5−32\frac{\sqrt{5} - \sqrt{3}}{2}

c)

5+32\frac{\sqrt{5} + \sqrt{3}}{2}

d)

−5+32-\frac{\sqrt{5} + \sqrt{3}}{2}

23.

Given a=7+2a = \sqrt{7} + 2 , b=37−2b = \frac{3}{\sqrt{7} - 2} , then the relationship between aa and bb is ( )

a)

A. ab=1ab = 1

b)

B. ab=−1ab = -1

c)

C. a=ba = b

d)

D. a=−ba = -b

24.

Th e graph shows the relationship between

temperature in degrees Celsius (°C) and degrees

Fahrenheit (°F).

Use the graph to convert:

a. 60 °C to (a)   °F

25.

Th e graph shows the relationship between

temperature in degrees Celsius (°C) and degrees

Fahrenheit (°F).

Use the graph to convert:

b. 16 °C to (a)   °F

26.

Th e graph shows the relationship between

temperature in degrees Celsius (°C) and degrees

Fahrenheit (°F).

Use the graph to convert:

c. 0 °F to (a)   °C

27.

Th e graph shows the relationship between

temperature in degrees Celsius (°C) and degrees

Fahrenheit (°F).

Use the graph to convert:

d. 100 °F to (a)   °C

28.

Convert £50 into Botswana pula, given that £1 = 9.83 pula.

(a)  

29.

Convert 803 pesos into British pounds given that £1 = 146 pesos.

(a)