Roots

Question 1

What is square root of 100?

Answer 1

10 (positive only)

Whenever root symbol is used, only consider the non-negative root of the number. The square root of a positive number will be positive. Positive root = principal square root.

Question 2

What is the square root of a variable squared?

Answer 2

The square root of a variable squared is equal to the absolute value of that variable.

Question 3

What is the square root of 0?

Answer 3

0

Question 4

Root 2

Answer 4

1.4

Question 5

Root 3

Answer 5

1.7

Question 6

Root 5

Answer 6

2.2

Question 7

Root 6

Answer 7

2.4

Question 8

Root 7

Answer 8

2.6

Question 9

Root 8

Answer 9

2.8

Question 10

Simplify root 200 + root 50

Answer 10

Root 200= root (100*2)
= 10 * root 2

Root 50= root (25*2)
= 5 * root 2

Sum = 15 * root 2

Question 11

Non-negative perfect cubes:
0
1
2
3
4
5
6
7
8
9
10

Answer 11

0
1
8
27
64
125
216
343
512
729
1000

Question 12

The cube root of a perfect cube is an integer or not an integer?

Answer 12

Integer

Question 13

The cube root of a non perfect cube is an integer or not an integer?

Answer 13

Not an integer

Question 14

Can a perfect cube be negative?

Answer 14

Yes eg -8

Question 15

13 ^2

Answer 15

169

Question 16

14^2

Answer 16

196

Question 17

15^2

Answer 17

225

Question 18

Is the square root of a perfect square a whole number?

Answer 18

Yes

Question 19

Is the square root of a non perfect square a whole number?

Answer 19

No

Question 20

Can a perfect square be negative?

Answer 20

No - can only be a whole number

Question 21

What is the index root of a variable to the power of the same index?

Answer 21

If the index is even and x is not negative, the answer is the absolute value of x (or always positive with the exception of 0)

If the index is odd the Answer is x.

Question 22

Can you combine radicals with different index numbers?

Answer 22

No

Question 23

How to simplify an expression with radicals in denominator?

Answer 23

Remove radical from denominator

Multiply the fraction by the radical over itself, multiply the fraction by the conjugate over itself

Question 24

When solving an equation involving roots, what must you always do?

Answer 24

Plug the answer back in just in case you have to reject an answer (eg if there are 2 answers)

Question 25

5^y=16

5^4y=

(Put in power of 2)

Answer 25

(5^y)^4 = (2^4)^4

= (2^16)

Question 26

Root 256

Answer 26

16

Question 27

5^5

Answer 27

3,125

Question 28

If x^102=100, which of the following must be the value of x^51?

Answer 28

X= -10 OR +10

Question 29

If a radical is a square root and a number x is under n such radicals, then as a power, what can it be written as?

So for example, 5 square rooted 4 times is what as a power?

Answer 29

X^(1/2^n)

5^(1/2^4) = 5^1/16