Surds & Indices

Question 1

What is a surd?

Answer 1

A surd is an irrational number that cannot be expressed as a simple fraction.

Question 2

True or False: The square root of 4 is a surd.

Answer 2

False

Question 3

What is the value of √9?

Answer 3

3

Question 4

Simplify: √50.

Answer 4

5√2

Question 5

What is the index law for multiplying powers with the same base?

Answer 5

Add the indices.

Question 6

Fill in the blank: The expression a^0 equals _____ for any non-zero number a.

Answer 6

1

Question 7

What is the value of 2^3?

Answer 7

8

Question 8

True or False: (a^m) * (a^n) = a^(m+n).

Answer 8

True

Question 9

Simplify: (x^2)^3.

Answer 9

x^6

Question 10

What is the value of 4^(1/2)?

Answer 10

2

Question 11

If x = 3, what is the value of x^4?

Answer 11

81

Question 12

What is the result of √(a^2)?

Answer 12

|a|

Question 13

What does the term ‘rationalizing the denominator’ mean?

Answer 13

It means to eliminate surds from the denominator of a fraction.

Question 14

True or False: The cube root of 27 is 3.

Answer 14

True

Question 15

What is the simplified form of √(x^4)?

Answer 15

x^2

Question 16

Calculate: 5^2 + 5^2.

Answer 16

50

Question 17

What is the index law for dividing powers with the same base?

Answer 17

Subtract the indices.

Question 18

Fill in the blank: The expression a^(-n) equals _____ for any non-zero number a.

Answer 18

1/a^n

Question 19

What is the value of 3^0?

Answer 19

1

Question 20

Simplify: √(x^2y^2).

Answer 20

xy

Question 21

If a = 2 and b = 3, what is the value of a^b?

Answer 21

8

Question 22

True or False: The product of two surds is always a surd.

Answer 22

False

Question 23

What is the simplified form of √(12)?

Answer 23

2√3

Question 24

Calculate: (2√3)(3√2).

Answer 24

6√6

Question 25

What is the value of 8^(1/3)?

Answer 25

2

Question 26

Simplify: (√2)^4.

Answer 26

4

Question 27

What is the result of 10^(1/2) * 10^(1/2)?

Answer 27

10