More Wiki Sections. Was this guide helpful? YES NO. In This Wiki Guide. Neverwinter Nights: Collector's Edition. Release Date. To find the natural number whose cube is the given number, take one factor fron each triple and multiply them. The cube of the number so obtained will be th, given number. Example2 Is a perfect cube? What is that number whose cube is ? What is the number whose cube is ? Therefore, is perfect cube. To determine the number whose cube is , we collect one factor from each group.
What is the smallest number by which product is a perfect cube? Thus, if we multiply by 7, 7 will also occur as a prime factor thrice and the product will be 2x2x 2x7x7x7, which is a perfect cube.
What is the smallest number by which must be divided so that 3 the quotient is a perfect cube? Therefore, quotient is a perfect cube. Prove that if a number is doubled, then its cube is eight times the cube of the given number.
Let b denote the double of a i. Evaluate tho following wy feat ere iy dio" atl! That is, odd, PHI on esas gy nyt Property 4 Cubes ofthe numbers ending in digite 1, 4,5, 6 and 9 are the numbers ending" the same digit. The cube of 2 ends in 8 and the cube of 8 ends in 2. Similarly, the cube of 3 ends in 7 and the cube of 7 ends in 3. Also, if a number ends in 0, then its cube will end in three zeros, 4. In this section, we will discuss column method for finding the cubes of two digit natural numbers.
The remaining procedure is exactly indentical to the method of finding the square of a two digit natural numbers, Following examples will illustrate the procedure.
Thus, - is also a perfect cube. Similarly, we define the cube of a rational number which is not an integer as given below. Also, find that rational number.
Find the cubes of ii 12 iii Which of the following numbers are cubes of negative integers i iii iv v - 3. Show that the following integers are cubes of negative integers. Also, find the integer whose cube is the given integer. Find which of the following numbers are cubes of rational numbers: 27 : da eee iii 0. Gill, iv, , In other words, the cube root of a number n is that number m whose cube gives Nn.
The cube root of a number n is denoted by Yn. Subtract 1 from it. If you get zero 1. Otherwise go to next step. Do you get 0 as the result, If yes, the cube root of the given number is 3. Do you get 0-as the vesult.
If yes, the cube root of the given number is 4. Otherwise, go to next step. Therefore, unite digit of its cube root is After striking out the last three digits from the right, the number left is Using the method of suecessive subtraction examine whether or not the following numbers are perfect cubes: i ii 3. Find the smallest number that mi question 2 which are not perfect cubes, to m corresponding cube roots?
Find the cube root of each of the following natural numbers: i ii iii , iv v yi vii viii ix x xi xii 5. Find the smallest number which when multiplied with will make the Produ perfect cube. Further, find the cube root of the product. Also, find the cube root of the quotient so obtained. Three numbers are in the ratio 1 : 2: 3.
The sum of their cubes is Find y, numbers. Find the side of the cube. Solution We have, 1. Find the length of a side of the box. Solution Let the length of a side of the box be x metres. Then, its volume is x cubic meters. But, the volume is given as Find the cube roots of each of the a ee ant i ii - iii - Show that. TxIs Id x18 8. The volume of a cubi i aay ical box is Find the length of each side Three numbers are t numbers.
The sum of their cubes is 0. Fin4" In fact, there are only ten numbers between 1 and which are perfect cubes. The remaining natural numbers are not perfect cubes.
Consequently, their cube roots are not whole numbers and they cannot be found exactly. These cube a and are therefore irrational numbers, Only approximate values of the cube roots of these numbers can be found. The third column gives multiplied by So, to find the cube root of 62, we look at the row containing 62 in the column of x. The following are some illustrations for the above assertions. Therefore, their sum when divided by!!
Let us now take a three digit number abe, By changi its digits i "i order, we obtain numbers bea and cab. Gili 37 iv 3. Interchanging its ones and hundreds digits, we get the number cba. Therefore, the difference between these two numb. Thus, the difference of a three digit number abc and the number obtained by interchangi its ones and hundreds digits ie.
Without performing actual addition and division write the quotient when the sum of 69 and 96 is divided by a 2.
Without performing actual computations, 9 Gi 5 3. If sum of the number and two other numbers obtained by arranging the digits of in eyelic order is divided by , 22 and 37 respectively. Find the quotient in each. Find the quotient when the differen: Gi 15 find the quotient when 94 - 49 is divided by. Mathematics for Clas. Also, problems on divisibility of the above mentioned divisors. Clearly, 10 is a multiple of 5. Therefore, 10a is also a multiple of 5.
Since the sum of any two multiples of 5 is a multiple of 5. Thus, an integer is divisible by 5, if its units digit is a multiple of 5. That is its units digit is either 0 or 5. So, we have the following test of divisibility by 5. It also follows from the above discussion that if the units digit of a number is not 0 or 5, then it is not divisible by 5.
Let n be any natural number. Thus, the remainder when an integer is divided by 5 is equal to the remainder when its units digit is divided by 5. For example, if is divided by 5, the remainder is 1.
Solution i If-n is divided by 5, then the remainder is equal to the remainder when its ones digit is divided by 5. Consequently, the units digit of n must be 3 or 8. So, the units digit of n is 1 or 6.
Since 10a is an even number and the sum of two even numbers is an even number and sum ofan even number and an odd number is an odd number. A number is divisible by 2, if its units digit isan even digit, , , or Since 10a is divisible by 2.
If the what might be the units digit of n? So, n must be an odd natnr. Hence, its units digit can be 1, 3, 5, 7, or 9. Hence, its units digit can be 0, 2,4, 6, or 8, 2, the remainder is zero if n is even, otherwise the remainder is 1. Wh must be the units digit of n? Solution It is given that the division of m by 5 leaves a remainder of 4.
Therefore, h: division of units digit of n by 5 must leave a remainder of 4. So, the units digi of nis either 4 or 9. It is also given that the division of n by 2 leaves a remainder of 1. So, its units digit can be 1, 3, 5, 7 or 9. Clearly, 9 is the common value of units digit in two cases, Hence, the units digit of n is 9. Uptill now, we have studied three tests of divisibility, In all the th is decided just by the units digit.
So, we have used only the units digit of the given number without even bothering about the rest of the number, This has happened because 10, 5 and 2 are divisors of 10, which is the key number in our place value system. Consider now a three digit number abe. Thus, we have following test of divisibility by 9.
It should be noted that a number is not divisible by 9 when the sum of its digits is not divisible by 9. It is evident from the above discussion that the remainder obtained by dividing a number by 9 is equal to the remainder when the sum of its digits is divided by 9. So, n is divisible by 9. So, m is not divisible by 9. Let us now discuss more illustrations on divisibility by 9. Solution Since 34q is divisible by 9. Therefore, the sum of its digits is a multiple , Since 21 ie.
But, y is a digit. Solution It is given that the number 2a25 is a multiple of 9. Therefore, the sum of digits is a multiple of 9. But, a is a digit. So,a can take values 0, J, 2, Since a multiple of 9 is also a multi i i : 4 multiple of 3, So, a natura visible by ifthe sum ofits digits is also divisible by 3. Nilesh Gupta. Shalih Abdul Qodir Qodir. Jaikumar Periyannan. Swaran Kanta. Bhishma Pandya. Nehal Goel. Gissele Abolucion.
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