Question 1/4
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (p) और (q) परिमेय संख्याएं हैं तथा \(p+q\sqrt{5}\) परिमेय है, तो (q) के बारे में क्या सही है?
If (p) and (q) are rational numbers and \(p+q\sqrt{5}\) is rational, what is true about (q)?
#rational-expression
#irrational-coefficient
#reasoning
A (q=0)
B (q=1)
C \(q=\sqrt{5}\)
D (q=p)
Explanation opens after your attempt
Step 1
Concept
If \(q\ne0\), then \(q\sqrt{5}\) is irrational and the sum cannot be rational. In exams check the possibility of a zero coefficient.
Step 2
Why this answer is correct
The correct answer is A. (q=0). If \(q\ne0\), then \(q\sqrt{5}\) is irrational and the sum cannot be rational. In exams check the possibility of a zero coefficient.
Step 3
Exam Tip
यदि \(q\ne0\), तो \(q\sqrt{5}\) अपरिमेय होगा और योग परिमेय नहीं हो सकता। परीक्षा में शून्य गुणांक की संभावना देखें।
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Question 2/4
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(12-\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(12-\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
A (m=225)
B (m=226)
C (m=227)
D (m=228)
Explanation opens after your attempt
Correct Answer
A. (m=225)
Step 1
Concept
\(\sqrt{225}=15\) is rational so \(12-\sqrt{225}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=225). \(\sqrt{225}=15\) is rational so \(12-\sqrt{225}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{225}=15\) परिमेय है इसलिए \(12-\sqrt{225}\) परिमेय होगा। पूर्ण वर्ग की जड़ परिमेय होती है।
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Question 3/4
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(5+\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(5+\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
A (m=121)
B (m=122)
C (m=123)
D (m=124)
Explanation opens after your attempt
Correct Answer
A. (m=121)
Step 1
Concept
\(\sqrt{121}=11\) is rational so \(5+\sqrt{121}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=121). \(\sqrt{121}=11\) is rational so \(5+\sqrt{121}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{121}=11\) परिमेय है इसलिए \(5+\sqrt{121}\) परिमेय होगा। पूर्ण वर्ग वाली जड़ परिमेय होती है।
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Question 4/4
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(9-\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(9-\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
A (m=100)
B (m=101)
C (m=102)
D (m=103)
Explanation opens after your attempt
Correct Answer
A. (m=100)
Step 1
Concept
\(\sqrt{100}=10\) is rational so \(9-\sqrt{100}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=100). \(\sqrt{100}=10\) is rational so \(9-\sqrt{100}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{100}=10\) परिमेय है इसलिए \(9-\sqrt{100}\) परिमेय होगा। पूर्ण वर्ग वाली जड़ परिमेय होती है।
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