5.1 Congruent Triangles 99 Mastery Practice Squares Square Roots Cubes Cube Roots 15 Mastery Practice 21
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2 Chapter - Squares, Square Roots, Cubes and Cube Roots. Squares. Square Roots 7. Cubes. Cube Roots 5 Mastery Practice Chapter - Rational and Irrational Numbers. Rational Numbers. Real Numbers 7. Operations Involving Surds 9 Mastery Practice 5 Chapter - Length and Area 7. Length 8. Area of Rectangles. Areas of Triangles, Parallelograms and Trapeziums 8. Estimation of Measurements 55 Mastery Practice 59 Chapter - Ratio, Proportion and Percentage 6. Ratio of Two Quantities 6. Proportion 67. Ratio of Three Quantities 7. Relationship between Percentages, Fractions and Decimals 8.5 Computations and Problems Involving Percentages 8 Mastery Practice 9 Chapter 5 - Congruent Triangles Congruent Triangles 99 Mastery Practice 06 Chapter 6 - Pythagoras Theorem Relationship between the Sides of a Right-angled Triangle Converse of Pythagoras Theorem Mastery Practice 7 Chapter 7 - Transformations 0 7. Transformation 7. Translation 7. Reflection 7. Rotation 7.5 Isometry Enlargement 5 Mastery Practice 67 Chapter 8 - Statistics 7 8. Pie Charts Obtaining and Interpreting Information from Pie Charts Solving Problems Involving Pie Charts 79 Mastery Practice 8 Chapter 9 - Probability Probability Scale Probability 90 Mastery Practice 9
3 Squares, Square Roots, Cubes and Cube Roots. 8 8 =. ( 6)( 6) =. 6 6 =. ( 5 ) ( 5 ) = = 6. ( )( )( ) = 7. = 8. ( 7 ) ( 7 ) ( 7 ) = 9. Change into improper fraction. (a) 8 (c) (b) 6 7 (d) By the end of this chapter, you should be able to explain and specify square roots and cube roots of real numbers. find square roots and cube roots of integral numbers by separating factors for the purpose of problem-solving as well as be aware of validity of the answers. explain results of finding square root and cube roots of integral numbers, fractions and decimals, and express the relationships between exponents and real numbers. find estimations of square root and cube root of real numbers, which can be applied for problem-solving, as well as be aware of validity of the answers. (d) (b) Answers: (c) 9. (a) Math Online Visit these websites to know more about this chapter: guide/square-roots-and-cube-roots. topicarticleid-666,articleid html maths/number/powersrootsrev.shtml Chapter Squares, Square Roots, Cubes and Cube Roots
4 . Squares A Stating a number multiplied by itself as a number to the power of two and vice versa The square of a number is the product you get when a number multiplied by itself. For example, the square of is = the square of is = 9 the square of 0.6 is 0.6 ( 0.6) = is read as five to the power of two of five squared or the square of five. If n is a number, then n n = n. n is also known as the base and as the exponent. For example, 5 5 = ( 0.7) = ( 0.7) = ( ) Write the following as a number to the power of two. (a) ( ) (b) (c) (a) ( ) (b) 0.7 (c) ( ) Expand each of the following as a number multiplied by itself. (a) 0 (b). (c) ( ) 7 (a) 0 0 (b).. (c) 7 7 Try Questions & in Test Yourself. Mathematic Mathayom
5 B Determining the squares of numbers To find the square of a number is to multiply the number by itself. Find the square of each of the following without using a calculator. (a) (b) 0. (c) The square of any number is greater than or equal to zero, that is, always positive. (a) (b) 0. (c) = ( ) = = = 9 = 0.0 = 6 When finding the square of a mixed number, the mixed number must be changed into an improper fraction first. Find each of the following. (a) ( ) (b) ( ) (a) ( ) (b) ( ) = ( ) 5 = ( 8 ) 5 6 = = 6 9 The values of ( ) and ( ) are different. ( ) = ( 5 5 ) = 5 6 Try Questions & in Test Yourself. C Estimating the squares of numbers Method : Approximation Round off the number to the nearest whole number that can be easily squared. Then, calculate the square of that whole number. Chapter Squares, Square Roots, Cubes and Cube Roots
6 Some fractions are required to be reduced to the lowest terms in order to find the square roots. For example, 8 = = = To find the square root of a mixed number, change the mixed number into an improper fraction. For example, = = = Try Question in Test Yourself. D Determining the square roots of decimals The square roots of certain decimals can be obtained by the following methods: By writing a decimal as the square of another decimal. For example, 0.09 = = 0. By changing a decimal into a fraction in which the numerator and the denominator are perfect squares. For example, 0.09 = 9 00 = 0 = 0. Try Question in Test Yourself. E Multiplying two square roots When we multiply two square roots of the same number, the product is the number itself. a a = ( a ) = a For example, = = When we multiply two square roots of different numbers, we get the square root of their product. a b = a b For example, 7 = 7 = Sometimes, the square root of a perfect square is obtained. For example, 8 = 6 = Try Question 5 7 in Test Yourself. 8 Mathematic Mathayom
7 . Cubes A Stating a number multiplied by itself twice as a number to the power of three and vice versa The cube of a number is the number multiplied by itself twice. For example, the cube of is = 8 the cube of 5 is 5 ( 5) ( 5) = 5 8 is read as eight to the power of three or eight cubed or the cube of eight. If m is a number, then m m m = m. m is also known as the base and as the exponent. For example, = 8 0. ( 0.) ( 0.) = ( 0.) = ( ) Try Questions and in Test Yourself. B Determining the cubes 5 Find the value of the following without using a calculator. (a) ( 9) (b) ( ) (a) ( 9) = 9 ( 9) ( 9) = 8 ( 9) = 79 (b) ( ) = = = 5 7 = 7 7 The cube of a negative number is always negative. Try Question in Test Yourself. Mathematic Mathayom
8 .. Write the following numbers as a number to the power of three. (a) (b) 0.6 ( 0.6) ( 0.6) (c) ( ) ( ) ( ). Write the following as a number multiplied by itself twice. (a) (b) ( ) 7 (c) (.5) 0. Find the value of each of the following. (a) 6 (b) 8 (c) 0. (d) (.5) (e) ( ) (f) ( ) 7. Estimate the value of each of the following. (a). (b) 508 (c) Estimate each of the following cubes by finding its range. (a) 7 (b) 5 (c) The diagram shows the net of a cube. If the area of the net is 86 cm, find the volume of the cube. 7. cm The diagram shows a cubical container which is filled with 750 cm of water. Find the volume of the empty space in the container. Mathematic Mathayom
9 Example Find the value of 7. 7 = 7 = Cube root of a negative number is always negative. Example Find the value of 6. 6 = 6 = 6 = Should find the cube roots of the numerator and denominator. approximation brackets cube cube root estimate expanded form fraction improper fraction lowest terms mixed numbers multiply negative numbers pair up perfect cube perfect square positive numbers power power of two power of three prime factorisation range round off square square root 0 Mathematic Mathayom
10 . Square of a = a a = a. The square of any number is always positive.. Perfect squares are squares of whole numbers. For example,,, 9, 6,. If a a = b, then b = a. 5. Cube of a = a a a = a 6. If a a a = b, then b = a. 7. The cube of a negative number is always negative. Objective Questions. Given that 5.9 = 9.09, then 909 = A 5.9 C 59. B 5.9 D = A 9 C B 6 D. Which of the following is not equal to 5? A ( 5 ) C (5) B 5 D ( 5). ( ) = 5 A C B D Given that.5 =. and 5 = 6.708, then = A 58.7 B 5.87 C 5.0 D = A 7 C 5 B D 7. Given that 8.7 = 9.076, then = A 8.7 C 870 B 87 D = A 9 C 0 B 6 D = 8 A C B D 0. The area of a square is 5 cm. The length 9 of each side of the square, in cm, is A 7 C 9 B 7 D 9 Chapter Squares, Square Roots, Cubes and Cube Roots
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