Is the product of two irrational numbers always irrational ? Justify your answer. -Maths 9th

1 Answer

Answer :

Solution  :- No, sometimes rational,sometimes irrational.

Related questions

Description : Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example. -Maths 9th

Last Answer : No, (xy) is necessarily an irrational only when x ≠0. Let x be a non-zero rational and y be an irrational. Then, we have to show that xy be an irrational. If possible, let xy be a rational number. Since ... wrong. Hence, xy is an irrational number. But, when x = 0, then xy = 0, a rational number.

Description : Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example. -Maths 9th

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Description : Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Last Answer : Take a = (2+ √3) and b =(2 - √3 ); a and b are irrational numbers, but their product = 4-3 = 1, is a rational number. Take c = √3 and d = -√3; c and d are irrational numbers. but their product = -3, is a rational number.

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Last Answer : Take a = (2+ √3) and b =(2 - √3 ); a and b are irrational numbers, but their product = 4-3 = 1, is a rational number. Take c = √3 and d = -√3; c and d are irrational numbers. but their product = -3, is a rational number.

Description : Classify the following numbers as rational or irrational and give justification of your answer. -Maths 9th

Last Answer : (i) 0.05918 is a rational number as decimal expansion is terminating. (ii)1.010010001.... is an irrational number as decimal expansion is non-terminating non-recurring(non-repeating). (iii) √9/27 = √1/3 = 1/ ... it is an irrational number. (iv) √12/75 = √4/25 = 2/5, which is a rational number.

Description : If the corresponding angles of two triangles are equal, then they are always. State true or false and justify your answer. -Maths 9th

Last Answer : Solution :- False, because two equilateral triangles with sides 3 cm and 6 cm respectively have all angles equal, but the triangles are not congruent.

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Last Answer : Root 3 root 5

Description : Find two irrational numbers between 2 and 2.5 . -Maths 9th

Last Answer : The two irrational numbers between 2 and 2.5 are 2.101001000100001----- and 2.201 001 0001 00001-----

Description : Find two irrational numbers between 0.1 and 0.12. -Maths 9th

Last Answer : The two irrational numbers between 0.1 and 0.12 are 0.1 010010001--- and 0.1101001000100001 -----

Description : Find two irrational numbers between ROOT 2 and ROOT 7. -Maths 9th

Last Answer : Root 3 root 5

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Last Answer : The two irrational numbers between 2 and 2.5 are 2.101001000100001----- and 2.201 001 0001 00001-----

Description : Find two irrational numbers between 0.1 and 0.12. -Maths 9th

Last Answer : The two irrational numbers between 0.1 and 0.12 are 0.1 010010001--- and 0.1101001000100001 -----

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Last Answer : There are infinite number of rational and irrational numbers between 2 and 3 .

Description : Identify the following as rational or irrational numbers .Give the decimal representation of rational numbers. -Maths 9th

Last Answer : In this way we can represent a rational numbers

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Last Answer : ∴ It is an irrational number .

Description : Examine whether the following numbers are rational or irrational: -Maths 9th

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Description : Find three irrational numbers between 2 and 2.5 . -Maths 9th

Last Answer : If a and b are any two distinct positive rational numbers such that ab is not a perfect square , then the irrational number √ab lies between a and b. ∴ Irrational number between 2 and 2.5 is √ 2 2.5 , i.e √5 Irrational number ... 2.5 are √5 , 2(1/2) 5(1/4) and (1/2) 5 3/4 21/2 .

Description : Let x and y be rational and irrational numbers, respectively. -Maths 9th

Last Answer : Yes, (x + y) is necessarily an irrational number.

Description : Classify the following numbers as rational or irrational with justification . -Maths 9th

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Description : How many rational numbers and irrational numbers can be inserted between 2 and 3 ? -Maths 9th

Last Answer : There are infinite number of rational and irrational numbers between 2 and 3 .

Description : Identify the following as rational or irrational numbers .Give the decimal representation of rational numbers. -Maths 9th

Last Answer : In this way we can represent a rational numbers

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Last Answer : Following are the rational numbers which represent irrational numbers .

Description : Examine , whether the following numbers are rational or irrational : -Maths 9th

Last Answer : ∴ It is an irrational number .

Description : Examine whether the following numbers are rational or irrational: -Maths 9th

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Description : Find three irrational numbers between 2 and 2.5 . -Maths 9th

Last Answer : If a and b are any two distinct positive rational numbers such that ab is not a perfect square , then the irrational number √ab lies between a and b. ∴ Irrational number between 2 and 2.5 is √ 2 2.5 , i.e √5 Irrational number ... 2.5 are √5 , 2(1/2) 5(1/4) and (1/2) 5 3/4 21/2 .

Description : Let x and y be rational and irrational numbers, respectively. -Maths 9th

Last Answer : Yes, (x + y) is necessarily an irrational number.

Description : Classify the following numbers as rational or irrational with justification . -Maths 9th

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Last Answer : Solution :-

Description : Give an example to show that the product of a rational number and an irrational number may be a rational number . -Maths 9th

Last Answer : A rational number 0 multiplied by an irrational number gives the irrational number 0.

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Last Answer : A rational number 0 multiplied by an irrational number gives the irrational number 0.

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Last Answer : Solution :- y-coordinate of both the points is 4. So, both points lie on the line y = 4 which is parallel to x-axis.

Description : State whether the following statements are true or false ? Justify your answer. -Maths 9th

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Description : Which of the following expressions are polynomials? Justify your answer, -Maths 9th

Last Answer : Following expressions are polynomials .

Description : Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Last Answer : (i) False, because a binomial has exactly two terms. (ii) False, because every polynomial is not a binomial . e.g., (a) 3x2 + 4x + 5 [polynomial but hot a binomial] (b) 3x2 + 5 [polynomial and also a binomial] (Hi ... = x4 + 2 + (-x4 + 4x3 + 2x) = 4x3 + 2x + 2 which is not a polynomial of degree 4.

Description : Write whether the following statements are true or false? Justify your answer. -Maths 9th

Last Answer : (i) False, since the ordinate of the point (3, 0) is zero. So, the point lies on X-axis. (ii) False, because in point (1, -1) x-coordinate is positive and y-coordinate is negative, so it lies ... -axis is 2 units. (v) True, because in a point (-1, 7) abscissa is negative and ordinate is positive.

Description : For what value of x + y in figure will ABC be a line? Justify your answer. -Maths 9th

Last Answer : For ABC to be a line, the sum of the two adjacent angles must be 180° i.e.,x + y = 180°.

Description : State whether the following statements are true or false ? Justify your answer. -Maths 9th

Last Answer : (i) False, here √2 is an irrational number and 3 is a rational number, we know that when we divide irrational number by non-zero rational number it will always give an irrational number. (ii) False, ... in the form p/q, q ≠0. p,q both are integers and these numbers are called irrational numbers.

Description : Which of the following expressions are polynomials? Justify your answer, -Maths 9th

Last Answer : Following expressions are polynomials .

Description : Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Last Answer : (i) False, because a binomial has exactly two terms. (ii) False, because every polynomial is not a binomial . e.g., (a) 3x2 + 4x + 5 [polynomial but hot a binomial] (b) 3x2 + 5 [polynomial and also a binomial] (Hi ... = x4 + 2 + (-x4 + 4x3 + 2x) = 4x3 + 2x + 2 which is not a polynomial of degree 4.

Description : Write whether the following statements are true or false? Justify your answer. -Maths 9th

Last Answer : (i) False, since the ordinate of the point (3, 0) is zero. So, the point lies on X-axis. (ii) False, because in point (1, -1) x-coordinate is positive and y-coordinate is negative, so it lies ... -axis is 2 units. (v) True, because in a point (-1, 7) abscissa is negative and ordinate is positive.

Description : For what value of x + y in figure will ABC be a line? Justify your answer. -Maths 9th

Last Answer : For ABC to be a line, the sum of the two adjacent angles must be 180° i.e.,x + y = 180°.

Description : Is every rational number a whole number?Justify your answer. -Maths 9th

Last Answer : No, for example 1/5 is a rational number but not a whole number.

Description : Write the coordinates of a point on x-axis at a distance of 6 units from the origin in the positive direction of x-axis and then justify your answer. -Maths 9th

Last Answer : Solution :- As, any point on x-axis has coordinates (,)x0 where x is the distance from origin, so required coordinates are (6, 0).

Description : The product of two different irrational numbers is always (a) rational (b) irrational (c) both of above (d) none of above

Last Answer : (b) irrational

Description : Insert a rational and an irrational number between 2 and 3. -Maths 9th

Last Answer : A rational number between 2 and 3 = 2 + 3 / 2 = 2.5 An irrational number between 2 and 3 is √5 .

Description : Which of the following is irrational ? -Maths 9th

Last Answer : Irrational number (c)

Description : Which of the following is irrational ? -Maths 9th

Last Answer : (d) An irrational number is non-terminating non-recurring which is 0.4014001400014….