Cube root is the inverse operation of a cube.
Symbol ∛ represents a cube-root.
e.g. $\sqrt[3]{8} = 2$,
$\sqrt[3]{216} = 6$
METHODS OF FINDING CUBE ROOT
There are two methods of finding Cube Root
1. Prime Factorisation
2. Estimation Method
Q1: Which of the following statements is wrong for viroids?
(a) They cause infections.
(b) Their RNA is of high molecular weight.
(c) They lack a protein coat.
(d) They are smaller than viruses.
Class 9 Maths - Important Identities
(a+b)² = a² + 2ab+ b²
(a–b)² = a² –2ab + b²
a² – b² = (a+b)(a–b)
Q1: Define nationalism.
Answer: The expression of Nationalism was brought about by the French revolution in 1789. Nationalism developed a sense of common identity and shared past or descent. Political movements and struggles by the leaders led to the current commonness. It emerged as a force to unify people which later led to the emergence of the nation-state.
Q2: Who was Frederic Sorrieu?
Answer: He was a French artist famous for a series of four prints prepared in 1848 that visualised the dream of a world consisting of ‘Democratic and Social Republics’.
RELATION
Let A and B be two nonempty sets. Then, a relation R from A to B is a subset of (A × B).
Thus, R is a relation from A to B ⇔ R ⊆ (A × B).
If (a, b) ∈ R then we say that ‘a is related to b‘ and we write, a R b.
If (a, b) ∉ R then ‘a is not related to b‘ and we write, $a \not \mathrel{R} b$.
Q1: Let A = {-1, 2, 4} and B = {1, 3}. Show A × B as arrow diagram.
A scatter plot also called scatter chart uses dots to represent data points for two different numeric variables. The position of each dot on the horizontal and vertical axis represent an individual data point.
A scatter plot is commonly used to compare distribution of two variables and to find visually any correlation between them. If there are distinct clusters/segments within the data, it will be clear in the scatter plot.
Let us try to plot a few scatter graphs using matplotlib.
A fraction is a part of whole.
Fractions are of various types. Commonly used fractions are mixed fractions, proper fractions
e.g. $ \frac{13}{4}, 2\frac{3}{4}, \frac{1}{2} $ etc.
COMPARE FRACTIONS
We can compare two or more fractions by taking the L.C.M of the denominators of the given fractions. Fraction with a greater denominator is bigger and vice versa.
Q1: Compare $\frac{23}{52} \textrm{ and } \frac{19}{22} $
Answer: $\frac{23}{52} > \frac{19}{22}$
Fill in the blanks in the following sentences with suitable word(s):
1. A collection of – 1, – 2, – 3, – 4, ... is called ________ integers.
2. Every positive integer is ________ than every negative integer.
3. Zero is ______ than every positive integer.
Q1: Simplify $\sqrt[4]{32}$ ?
Answer:
$\sqrt[4]{32} = \left ( 32 \right )^{\frac{1}{4}} $
$= \left ( 2^5 \right )^{\frac{1}{4}}$
$ = \left ( 2^4 . 2^1 \right )^{\frac{1}{4}} $
$= \left ( 2^4 \right )^{\frac{1}{4}}.(2)^{\frac{1}{4}}$
$= 2.\sqrt[4]{2}$
Q1: Define life span.
Answer: Life span is the period from birth to the natural death of an organism.
Q2: What is the life span of the following organisms?
(a) Mayfly
(b) Human Being
(c) Parrot
(d) Rice Plant
(e) Sequoia Trees
(f) Butterfly
Answer:
(a) Mayfly - 1 day
(b) Human Being - 100 years
(c) Parrot - 140 years
(d) Rice Plant - 3 to 4 months
(e) Sequoia Trees - 3000 to 4000 years
(f) Butterfly - 1 to 2 weeks
