Topik 2 matematik T2

7/29/2019 Topik 2 matematik T2

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MATHEMATICS - FORM 2

SQUARES, SQUAREROOTS, CUBES AND CUBEROOTS


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SQUARES OF NUMBERS

(A) Stating the square of a number

1. The square of number is a product of the number multiplied by itself.

2. The square of a number can be written either in the expanded form or the index form (with thesquare notation (

2)).

For example :

3. The square of any number is always positive.


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For example:

4. The square of a number can be read in several ways.For example :

242

is read as(i) twenty-four to the power of two(ii) twenty-four squared(iii) the square of twenty-four

5. a is an index form for a x a and is not equal to a x 2.For example :


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(B) Determining the squares of numbers without using a calculator

1. The value of the square of a number can be obtained by multiplying the number by itself.For example,

2. The number of decimal places (d.p) in the square of a decimals is twice the number of decimalplaces of the decimal being squared.For example :

3. A mixed number has to be changed to an improper fraction before squaring.For example :


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(C) Estimating the squares of numbers

There are two methods that can be used to estimate the squares of numbers.


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Method 1: By approximation

Round off the number to the nearest whole number or to one decimal point that can be easily squared.For example:

Method 2: By determaining the range

The square of a number can be estimated by stating it between two values that can be easily squared.

(D) Determining the squares of numbers using a calculator

1. To determine the square of a number by using a calculator, press the number keys followedby the X

2key on the calculator.

2. Different models of calculators have different buttons for squaring a number.For example:

3. By pressing a number, then Xfollowed by pressing the number again, we can also determine thesquare of the number.For example:


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4. There are other function keys that will be used to determine the squares of the directed numbers.

5. For square values that exceed 10 digits, the reading on a calculator is an approximation.


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same factors.

3. Perfect squares are whole numbers. Thus, decimals and fractions are not perfect squares.

(G) Solving problems involving squares of numbers


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SQUARE ROOTS OF NUMBERS

(A) Writing the Square Roots of a Positive Number


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(B) Determining the Square Roots of Perfect Squares Without Using a Calculator

Finding the square root of a number is the inverse process (opposite) of squaring.


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(C) Determining the Square Roots of Positive Numbers Without Using a Calculator

The square root of a fraction is computed by finding the square root of the numerator and the denominator.Example :

Some fractions are reduced to lowest terms in order to find their square roots.Example :

To find the square root of a mixed number, change it to an improper fraction first.Example :


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The square root of a decimal can be found by changing the decimal to a fraction and then finding the squareroot of its numerator and denominator.Example :


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(D) Multiplying Two Square Roots

The product of two square roots of the same number will produce the number itself.

Example :

The product of two square roots of two different numbers can be found by multiplying the two numbers firstand then finding its square root.

Example :


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(E) Estimating the Square Roots of Numbers

Method 1 : Estimating to the Nearest Value

Round off the given number to the nearest whole number from which the square root can be found easily.

Method 2 : Stating the Square Root of a Number Between Two Values Determiningthe range of the square root of a number

The square root of a number can be estimated between two values (the range), from which the square root


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can be found easily.

(F) Finding the Square Roots of Numbers Using a Scientific Calculator


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(G) Solving Problems Involving Squares and Square Roots


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CUBES OF NUMBERS

(A) Stating the cube of a number

1. The cube of a number is the product of the number multiplied by itself twice.

2. The symbol of cube is ' '. The cube can be represented in two ways, that are the expandedform and the index form.For example :


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3. The cube of numbers can be read in several ways.For example :

5 is read as(i) five cubed(ii) five to the power of three(iii) the cube of five

(B) Determining cubes of numbers without using a calculator

1. The value of a cubed number can be obtained by multiplying the given number by itself twice. Forexample :

(- 6) = - 6 x ( - 6 ) x ( - 6 )= 36 x ( - 6 )= - 216

2. The cube value of a positve number always positive.

3. The cube value of a negative number always negative.


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(C) Estimating the cubes of numbers

Like the square and square root, we can estimate the cube of a number by approximation or by determiningthe range where the value of the cube lies.


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(E) Solving problems involving cubes of numbers

CUBE ROOTS OF NUMBERS

(A) Writing the Cube Root of a Number

The cube root of any given number is the number that, when multiplied by itself twice, is equal to the given


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number.


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(B) Estimating the Cube Roots of Numbers

Method 1: Estimating to the Nearest Value

Method 2: Stating the Cube Root of a Number Between Two Values Determining the

range of the cube root of a number.


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(C) Determining the Cube Roots of Integers Without Using a Calculator

(D) Determining the Cube Roots of Numbers Without Using a Calculator


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(E) Determining the Cube Roots of Numbers Using a Calculator

(F) Solving Problems Involving Cubes and Cube Roots


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(G) Computations Involving Addition, Subtraction, Multiplication, Division andMixed Operations on Squares, Square Roots, Cubes and Cube Roots

When performing mixed operations on squares, square roots, cubes and cube roots, follow the order of operations asbelow.

(a) Carry out the operations in the brackets [( )] first.

(b) Next, multiply or divide; calculating from left to right.

(c) Finally, add or subtract; again calculating from left to right.


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