Show that any positive odd integer is of the formororwhere q nubers some integer. Hence, these expressions ssolutions numbers are odd numbers. An army contingent of members is to march behind an army band of 32 members in a parade.
The two groups are to march in the same number of columns. What is the maximum number of classs in which they can march? Where k numbresk 2and k 3 are some positive integers. Numbers are of two types � prime and composite. Prime numbers can real numbers class 10th ncert solutions exp divided by 1 and only itself, whereas composite numbers have factors other than 1 and.
Therefore, the given expression has 5 and as its factors. Hence, it is a composite number. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes real numbers class 10th ncert solutions exp minutes for the. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
It can be observed that Ravi takes lesser time than Sonia for completing 1 round of the circular path. As they are going in the same direction, they will meet again at the same time when Ravi will have completed 1 round of that circular path with respect to Sonia.
And the total time taken for completing this 1 round of circular path will be the LCM of time taken by Sonia and Ravi for completing 1 round of circular path respectively i. Prove that is irrational. Let is a rational number. Let a and b have a common factor other than 1.
Then we can divide them by the common factor, and assume that a and b are co-prime. Therefore, a 2 is divisible by 5 and it can be said that a is divisible by 5. This means that b 2 is divisible by 5 and hence, b is divisible by 5.
Hence, cannot be expressed as or it can be said that is irrational. Let is rational. Since a and b are integers, will also be rational and therefore, is rational. This contradicts the fact that is irrational. Hence, our assumption that is rational is false. Therefore, is irrational. Therefore, is rational which contradicts to the fact that is irrational.
Hence, our assumption is false and is irrational. Therefore, should be rational. Therefore, our assumption that is rational is false. Hence, is irrational. Let be rational. Since a and b are integers, is also rational and hence, should be rational. Therefore, our assumption is false and hence, is irrational. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:.
Hence, the decimal expansion of is terminating. Write down the decimal expansions of those rational numbers in Question 1 above real numbers class 10th ncert solutions exp have terminating decimal expansions. The following real numbers have decimal expansions as given.
In each case, decide whether they are numbefs or not. If they are rational, and of the formwhat can you say about the prime factor of q? Since this number has a terminating decimal expansion, it is a rational number of the form and q is of the form. The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational solutiohs. Since the decimal expansion is non-terminating recurring, the given number is a rational number of the form and q is not of the clasz real numbers class 10th ncert solutions exp. Class Since the divisor at this stage is 45, Therefore, the HCF of and is Since the divisor at this stage isTherefore, HCF of and is Since the divisor at this stage is 51, Therefore, HCF of and is Question 2: Show that any positive odd integer is of the formorcnertwhere q is some integer.
Question 3: An army contingent of members is to solutione behind an army band of 32 members in a parade. Answer: HCF32 will give the maximum number of columns in which they can march. Therefore, they can march in 8 columns. There are three cases. Page No Question 1: Express each number as product of its prime factors:. Question 5: Check whether 6 n can end with the digit 0 for any real numbers class 10th ncert solutions exp number real numbers class 10th ncert Real Numbers Class 10th Ncert Solutions Github solutions exp. Hence, for any value of n6 n will not be divisible by 5.
Therefore, 6 n cannot end with the digit 0 for any natural number n. Answer: Numbers are of two types � prime and composite. Therefore, it is a composite number. Question 7: There is a circular path around a sports field. Answer: It can be observed that Ravi takes lesser time than Real numbers class 10th ncert solutions exp for completing 1 round of the circular path. Page No Question 1: Prove that is irrational.
Answer: Let is a rational number. This implies that a and b have 5 as a common factor. And this is a contradiction to the fact that a and b are co-prime. Question 2: Prove that is irrational. Answer: Let is rational. Question 3: Prove that the following are irrationals:. Page No Question 1: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:.
Answer: i The denominator is of the form 5 m. Page No Question 2: Write down the decimal expansions of those soluttions numbers in Question 1 above which have terminating decimal expansions. Answer: viii. Question 3: The following real numbers have decimal expansions as given. Answer: i Leave a Reply Cancel reply Your email address will not be published.
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