Roots Flashcards
What is square root of 100?
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.
What is the square root of a variable squared?
The square root of a variable squared is equal to the absolute value of that variable.
What is the square root of 0?
0
Root 2
1.4
Root 3
1.7
Root 5
2.2
Root 6
2.4
Root 7
2.6
Root 8
2.8
Simplify root 200 + root 50
Root 200= root (100*2)
= 10 * root 2
Root 50= root (25*2)
= 5 * root 2
Sum = 15 * root 2
Non-negative perfect cubes: 0 1 2 3 4 5 6 7 8 9 10
0 1 8 27 64 125 216 343 512 729 1000
The cube root of a perfect cube is an integer or not an integer?
Integer
The cube root of a non perfect cube is an integer or not an integer?
Not an integer
Can a perfect cube be negative?
Yes eg -8
13 ^2
169
14^2
196
15^2
225
Is the square root of a perfect square a whole number?
Yes
Is the square root of a non perfect square a whole number?
No
Can a perfect square be negative?
No - can only be a whole number
What is the index root of a variable to the power of the same index?
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.
Can you combine radicals with different index numbers?
No
How to simplify an expression with radicals in denominator?
Remove radical from denominator
Multiply the fraction by the radical over itself, multiply the fraction by the conjugate over itself
When solving an equation involving roots, what must you always do?
Plug the answer back in just in case you have to reject an answer (eg if there are 2 answers)
5^y=16
5^4y=
(Put in power of 2)
(5^y)^4 = (2^4)^4
= (2^16)
Root 256
16
5^5
3,125
If x^102=100, which of the following must be the value of x^51?
X= -10 OR +10
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?
X^(1/2^n)
5^(1/2^4) = 5^1/16
