hi i am teacher daisy now let's learn form 1 mathematics chapter 3 squares square roots cube and cube roots in this chapter you will learn 3.1 squares and square root 3.2 cubes and cube roots 3.1 squares and square root perfect square perfect square is a number made by squaring a whole number for example two squared is two repeated multiply for two times three squared is three repeated multiply for two times four squared is four repeated multiply for two times five squared is five repeated multiply for two times determine whether a number is a perfect square we can use the method of prime factorization to determine whether a number is a perfect square in this method if the prime factors can be grouped into two identical groups then the number is a perfect square example determine whether each of the following numbers is a perfect square a 36 b 54 solution a 36 can be divided by four and nine four can be further divided by two and two while nine can be further divided by three three thirty-six equals two times three times two times three these prime factors can be grouped into two identical groups thus 36 is a perfect square b 54 can be divided by six and nine six can be further divided by two and three while nine can be further divided by three and three fifty-four equals two times three times 3 times 3 these prime factors cannot be grouped into two identical groups thus 54 is not a perfect square relationship between squares and square roots three squared equals three times three equals nine square root of nine equals three determine the square of a number example find the value of each of the following without using a calculator solution a six squared equals six times six equals thirty-six be three over four squared equals three over four times three over four equals nine over sixteen c negative zero point five squared equals negative 0.5 times negative 0.5 equals 0.25 determine the square root of a number example find the value of each of the following without using a calculator solution a square root of 64 equals square root of eight times eight equals eight b 441 equals 3 times 3 times 7 times 7 equals 3 times 7 times 3 times 7 equals 21 times 21 square root 441 equal square root 21 times 21 equals 21. example find the value of each of the following without using a calculator solution a square root of 4 over 25 equals square root of 2 over 5 times 2 over 5 equals square root of two over five square equals two over five b square root of two and seven over nine equals square root of 25 over nine equals square root of five over three times five over three equals square root of five over three square equals five over three c square root of zero point three six equals square root of 0.6 times 0.6 equals square root of 0.6 square equals 0.6 example calculate the value of each of the following by using a calculator and give your answer correct to two decimal places solution a square root 89 equals 9.43 in two decimal places b square root 154.7 equals 12.44 in two decimal places see square root of six and two over seven equals two point five one in two decimal places estimate the square and square root of a number if we do not have a calculator and want to roughly know the value we estimate example estimate the value of a 27.5 squared b square root of 54. solution a 27.5 is between 20 and 30. 27.5 squared is between 20 squared and 30 squared 27.5 squared is between 400 and 900. thus 27.5 squared approximate to 900. b 54 is between perfect squares 49 and 64. square root of 54 is between square root of 49 and square root of 64. that is square root of 54 is between 7 and 8. thus square root of 54 approximate to 7. generalization can be made when two square roots are multiplied the product of two equal square root numbers is the number itself that is square root of a times square root of a equals a for instance square root of two times square root of two equals two the product of two different square root numbers is the square root of the product of the two numbers that is square root of a times square root of b equals square root of a b for instance square root of two times square root of three equals square root of two times three equals square root of six 3.2 cubes and cube roots perfect cube perfect cube is a number made by multiplying a whole number three times for example 2 cubed is 2 repeated multiply for 3 times 3 cubed is 3 repeated multiply for 3 times determine whether a number is a perfect cube we can also use the method of prime factorization to determine whether a number is a perfect cube in this method if the prime factors can be grouped into three identical groups then the number is a perfect cube example determine whether each of the following numbers is a perfect cube a 64 b 240 solution a 64 can be divided by eight times eight eight can be further divided by four and two and then four can be divided by two and two sixty four equals two times two times two times two times two times two these prime factors can be grouped into three identical groups thus 64 is a perfect cube b 240 can be divided by 12 and 20. 12 can be divided by 4 and 3 and 20 can be divided by four and five four can be further divided by two and two 240 equals two times two times three times two times two times five since these prime factors cannot be grouped into three identical groups thus 240 is not a perfect cube relationship between cubes and cube roots three cubed equals three times three times three equals twenty-seven cube root of twenty-seven equals three determine the cube of a number example find the value of each of the following without using a calculator solution a 4 cubed equals 4 times 4 times 4 equals 64. b 0.2 cubed equals 0.2 times 0.2 times 0.2 equals 0.00 c negative three-fifths cubed equals negative three-fifths times negative three-fifths times negative three-fifths equals negative 27 125 example find the value of each of the following using a calculator solution a 18q 5832 b negative 4 and 1 over 2 cubed equals negative 91 and one over eight c negative six point three cubed equals negative 250.047 [Music] determine the cube root of a number example find the value of each of the following without using a calculator solution a cube root of 64 equals cube root of four times four times four equals cube root of four cubed equals four b 216 equals two times two times three times three times two times three equals three times two times three times two times three times two equals six times six times six cube root of 216 equals cube root of six times six times six equals cube root of six cubed equals six example find the value of each of the following without using a calculator solution a cube root of 0.027 equals cube root of 0.3 cubed equals 0.3 b cube root of negative 0.008 equals cube root of negative 0.2 cubed equals negative 0.2 example find the value of each of the following without using a calculator [Music] solution a cube root of 8 over 125 equals cube root of two-fifths times two-fifths times two-fifths equals cube root of two-fifths cubed equals two-fifths b cube root of negative eighty-one over one hundred ninety-two simplify the fraction first equals cube root of negative 27 over 64 equals cube root of negative three quarters times negative three quarters times negative three-quarters equals cube root of negative three-quarters cubed equals negative three-quarters c cube root of three and three-eighths convert to improper fraction first equals cube root of 27 eighths equals cube root of three over two times three over two times three over two equals cube root of three over two cubed equals three over two equals one and one over two example calculate the value of each of the following by using a calculator give your answer corrected two decimal places solution a cube root of 24 equals 2.88 b cube root of negative 104.8 equals negative four point seven one c cube root of negative one and two ninths equals negative one point zero seven estimate the cube and cube root of a number if we do not have a calculator and want to roughly know the value we estimate example estimate the value of a 4.2 cubed b cube root of 180 solution a 4.2 is between 4 and 5. 4.2 cubed is between 4 cubed and 5 cubed 4.2 cubed is between 64 and 125 thus 4.2 cubed is approximate to 64. b 180 is between perfect cubes 125 and 216. cube root of 180 is between cube root of 125 and cube root of 216. cube root of 180 is between 5 and 6. cube root of 180 is approximate to 6. the concept map of form 1 chapter 3 is as below if you find this video helpful don't forget to like share and subscribe our channel and if you got any question can comment below thanks for watching