90423
Classify the following numbers as rational or irrational : \(2-\sqrt{5}\)
1 )Irrational number
2 )Rational number
3 )Less Data
4 )None of the above
Explanation:
Exp: A Irrational number Solution 2 is rational Click and drag to move ......... which is non terminating and non repeating hence irrational number. We know that, rational − irrational = irrational number. Hence 2 - 5 = irrational number
REAL NUMBERS
90425
Which of the following has terminating decimal expansion?
1 )\(\frac{32}{91}\)
2 )\(\frac{19}{80}\)
3 )\(\frac{23}{45}\)
4 )\(\frac{25}{42}\)
Explanation:
Exp: B \(\frac{19}{80}\) A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. \(\frac{32}{91}=\frac{32}{7\times13}\) \(\frac{19}{80}=\frac{19}{2^4\times5}\) \(\frac{23}{45}=\frac{23}{3^2\times5}\) \(\frac{25}{42}=\frac{25}{2\times3\times7}\) Clearly, option (b) is a terminating decimal, since its denominator is of the form 2\(^{m}\) × 5\(^{n}\) Never Active Medium **[Real Numbers]**
REAL NUMBERS
90426
If a and b are both positive rational numbers, then \(\big(\sqrt{\text{a}}+\sqrt{\text{b}}\big)\big(\sqrt{\text{a}}-\sqrt{\text{b}}\big)\) is:
1 )neither rational nor rational number
2 )none of these
3 )an irrational number
4 )a rational number
Explanation:
Exp: D a rational number \(\bigg(\sqrt{\text{a}}+\sqrt{\text{b}}\bigg)\bigg(\sqrt{\text{a}}-\sqrt{\text{b}}\bigg)\)=\(\Big\{(\sqrt{\text{a}})^2-\big(\sqrt{\text{b}})^2\Big\}\) = (a - b) Since a and b both are positive rational numbers, Therefore, the difference of two positive rational numbers is also rational.
REAL NUMBERS
90427
The number 3.24636363... is:
1 )An integer.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: B A rational number. 3.24636363... Which is repeating decimal number, and hence is a rational number. Never Active
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REAL NUMBERS
90423
Classify the following numbers as rational or irrational : \(2-\sqrt{5}\)
1 )Irrational number
2 )Rational number
3 )Less Data
4 )None of the above
Explanation:
Exp: A Irrational number Solution 2 is rational Click and drag to move ......... which is non terminating and non repeating hence irrational number. We know that, rational − irrational = irrational number. Hence 2 - 5 = irrational number
REAL NUMBERS
90425
Which of the following has terminating decimal expansion?
1 )\(\frac{32}{91}\)
2 )\(\frac{19}{80}\)
3 )\(\frac{23}{45}\)
4 )\(\frac{25}{42}\)
Explanation:
Exp: B \(\frac{19}{80}\) A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. \(\frac{32}{91}=\frac{32}{7\times13}\) \(\frac{19}{80}=\frac{19}{2^4\times5}\) \(\frac{23}{45}=\frac{23}{3^2\times5}\) \(\frac{25}{42}=\frac{25}{2\times3\times7}\) Clearly, option (b) is a terminating decimal, since its denominator is of the form 2\(^{m}\) × 5\(^{n}\) Never Active Medium **[Real Numbers]**
REAL NUMBERS
90426
If a and b are both positive rational numbers, then \(\big(\sqrt{\text{a}}+\sqrt{\text{b}}\big)\big(\sqrt{\text{a}}-\sqrt{\text{b}}\big)\) is:
1 )neither rational nor rational number
2 )none of these
3 )an irrational number
4 )a rational number
Explanation:
Exp: D a rational number \(\bigg(\sqrt{\text{a}}+\sqrt{\text{b}}\bigg)\bigg(\sqrt{\text{a}}-\sqrt{\text{b}}\bigg)\)=\(\Big\{(\sqrt{\text{a}})^2-\big(\sqrt{\text{b}})^2\Big\}\) = (a - b) Since a and b both are positive rational numbers, Therefore, the difference of two positive rational numbers is also rational.
REAL NUMBERS
90427
The number 3.24636363... is:
1 )An integer.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: B A rational number. 3.24636363... Which is repeating decimal number, and hence is a rational number. Never Active
90423
Classify the following numbers as rational or irrational : \(2-\sqrt{5}\)
1 )Irrational number
2 )Rational number
3 )Less Data
4 )None of the above
Explanation:
Exp: A Irrational number Solution 2 is rational Click and drag to move ......... which is non terminating and non repeating hence irrational number. We know that, rational − irrational = irrational number. Hence 2 - 5 = irrational number
REAL NUMBERS
90425
Which of the following has terminating decimal expansion?
1 )\(\frac{32}{91}\)
2 )\(\frac{19}{80}\)
3 )\(\frac{23}{45}\)
4 )\(\frac{25}{42}\)
Explanation:
Exp: B \(\frac{19}{80}\) A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. \(\frac{32}{91}=\frac{32}{7\times13}\) \(\frac{19}{80}=\frac{19}{2^4\times5}\) \(\frac{23}{45}=\frac{23}{3^2\times5}\) \(\frac{25}{42}=\frac{25}{2\times3\times7}\) Clearly, option (b) is a terminating decimal, since its denominator is of the form 2\(^{m}\) × 5\(^{n}\) Never Active Medium **[Real Numbers]**
REAL NUMBERS
90426
If a and b are both positive rational numbers, then \(\big(\sqrt{\text{a}}+\sqrt{\text{b}}\big)\big(\sqrt{\text{a}}-\sqrt{\text{b}}\big)\) is:
1 )neither rational nor rational number
2 )none of these
3 )an irrational number
4 )a rational number
Explanation:
Exp: D a rational number \(\bigg(\sqrt{\text{a}}+\sqrt{\text{b}}\bigg)\bigg(\sqrt{\text{a}}-\sqrt{\text{b}}\bigg)\)=\(\Big\{(\sqrt{\text{a}})^2-\big(\sqrt{\text{b}})^2\Big\}\) = (a - b) Since a and b both are positive rational numbers, Therefore, the difference of two positive rational numbers is also rational.
REAL NUMBERS
90427
The number 3.24636363... is:
1 )An integer.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: B A rational number. 3.24636363... Which is repeating decimal number, and hence is a rational number. Never Active
90423
Classify the following numbers as rational or irrational : \(2-\sqrt{5}\)
1 )Irrational number
2 )Rational number
3 )Less Data
4 )None of the above
Explanation:
Exp: A Irrational number Solution 2 is rational Click and drag to move ......... which is non terminating and non repeating hence irrational number. We know that, rational − irrational = irrational number. Hence 2 - 5 = irrational number
REAL NUMBERS
90425
Which of the following has terminating decimal expansion?
1 )\(\frac{32}{91}\)
2 )\(\frac{19}{80}\)
3 )\(\frac{23}{45}\)
4 )\(\frac{25}{42}\)
Explanation:
Exp: B \(\frac{19}{80}\) A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. \(\frac{32}{91}=\frac{32}{7\times13}\) \(\frac{19}{80}=\frac{19}{2^4\times5}\) \(\frac{23}{45}=\frac{23}{3^2\times5}\) \(\frac{25}{42}=\frac{25}{2\times3\times7}\) Clearly, option (b) is a terminating decimal, since its denominator is of the form 2\(^{m}\) × 5\(^{n}\) Never Active Medium **[Real Numbers]**
REAL NUMBERS
90426
If a and b are both positive rational numbers, then \(\big(\sqrt{\text{a}}+\sqrt{\text{b}}\big)\big(\sqrt{\text{a}}-\sqrt{\text{b}}\big)\) is:
1 )neither rational nor rational number
2 )none of these
3 )an irrational number
4 )a rational number
Explanation:
Exp: D a rational number \(\bigg(\sqrt{\text{a}}+\sqrt{\text{b}}\bigg)\bigg(\sqrt{\text{a}}-\sqrt{\text{b}}\bigg)\)=\(\Big\{(\sqrt{\text{a}})^2-\big(\sqrt{\text{b}})^2\Big\}\) = (a - b) Since a and b both are positive rational numbers, Therefore, the difference of two positive rational numbers is also rational.
REAL NUMBERS
90427
The number 3.24636363... is:
1 )An integer.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: B A rational number. 3.24636363... Which is repeating decimal number, and hence is a rational number. Never Active