radicals se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
44 questions tagged with radicals.
What is the value of (b) in \(x^2+6\sqrt{5}x+45=0\)?
A. \(6\sqrt{5}\)
(x) के साथ लगा गुणांक \(6\sqrt{5}\) है। करणी वाले गुणांक भी चिन्ह सहित लिखें। / The coefficient attached to (x) is \(6\sqrt{5}\). Write radical coefficients with their signs too.
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What is the value of (b) in \(x^2-4\sqrt{2}x+8=0\)?
A. \(-4\sqrt{2}\)
(x) के साथ लगा गुणांक \(-4\sqrt{2}\) है। करणी वाले गुणांक में भी चिन्ह साथ रखें। / The coefficient attached to (x) is \(-4\sqrt{2}\). Keep the sign with radical coefficients too.
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What is the value of (b) in \(x^2+2\sqrt{3}x+3=0\)?
A. \(2\sqrt{3}\)
(x) के साथ लगा गुणांक \(2\sqrt{3}\) है। करणी वाले गुणांक भी सामान्य गुणांक की तरह लिए जाते हैं। / The coefficient attached to (x) is \(2\sqrt{3}\). Radical coefficients are treated like ordinary coefficients.
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If \(x=\sqrt{3}+\sqrt{2}\), which quadratic equation does (x) satisfy?
C. \(x^4-10x^2+1=0\)
\(x^2=5+2\sqrt{6}\) और फिर (\(x^2-5\)2=24), इसलिए \(x^4-10x^2+1=0\) है। परीक्षा में दो वर्गमूलों के योग से कभी द्विघात नहीं बल्कि चतुर्थ घात संबंध भी बन सकता है। / Here \(x^2=5+2\sqrt{6}\) and then (\(x^2-5\)2=24), so \(x^4-10x^2+1=0\). In exams a sum of two radicals may lead to a fourth-degree relation.
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If \(\alpha=\sqrt{12}\) and \(\beta=-\sqrt{3}\), what is \(\alpha+\beta\)?
A. \(\sqrt{3}\)
\(\sqrt{12}=2\sqrt{3}\), इसलिए \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\)। करणी सरल करना जरूरी है। / \(\sqrt{12}=2\sqrt{3}\), so \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\). Simplifying radicals is important.
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Which option is equal to \(2\sqrt{15}\)?
B. \(\sqrt{60}\)
\(2\sqrt{15}=\sqrt{4}\sqrt{15}\) लिखा जा सकता है। / \(2\sqrt{15}=\sqrt{4}\sqrt{15}\).
इसलिए \(2\sqrt{15}=\sqrt{60}\)। / Therefore \(2\sqrt{15}=\sqrt{60}\).
गुणांक को मूल के अंदर ले जाते समय उसका वर्ग अंदर जाता है। / When moving a coefficient inside a square root, its square goes inside.
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What is the nature of \(\sqrt{7}+\sqrt{28}+\sqrt{63}\)?
B. अपरिमेयIrrational
\(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{63}=3\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{63}=3\sqrt{7}\).
कुल योग \(6\sqrt{7}\) है, जो अपरिमेय है। / The total is \(6\sqrt{7}\), which is irrational.
किसी अभिव्यक्ति की प्रकृति तय करने से पहले उसे सरल करें। / Simplify an expression before deciding its nature.
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What is the nature of \(\sqrt{5}+\sqrt{20}+\sqrt{45}\)?
B. अपरिमेयIrrational
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
कुल योग \(6\sqrt{5}\) है, जो अपरिमेय है। / The total is \(6\sqrt{5}\), which is irrational.
किसी अभिव्यक्ति की प्रकृति तय करने से पहले उसे सरल करें। / Simplify an expression before deciding its nature.
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What is the nature of \(\sqrt{3}+\sqrt{12}+\sqrt{27}\)?
B. अपरिमेयIrrational
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\).
कुल योग \(6\sqrt{3}\) है, जो अपरिमेय है। / The total is \(6\sqrt{3}\), which is irrational.
सरलीकरण के बाद ही संख्या की प्रकृति तय करें। / Decide the nature of the number only after simplification.
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Which of the following results is rational?
B. \(\sqrt{2}\times\sqrt{8}\)
\(\sqrt{2}\times\sqrt{8}=\sqrt{16}\) होता है। / \(\sqrt{2}\times\sqrt{8}=\sqrt{16}\).
\(\sqrt{16}=4\), जो परिमेय संख्या है। / \(\sqrt{16}=4\), which is rational.
दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता। / The product of two irrational numbers is not always irrational.
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Which of the following results is irrational?
B. \(\sqrt{7}+\sqrt{28}\)
\(\sqrt{28}=2\sqrt{7}\), इसलिए \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), so \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\).
\(3\sqrt{7}\) अपरिमेय है क्योंकि \(\sqrt{7}\) अपरिमेय है। / \(3\sqrt{7}\) is irrational because \(\sqrt{7}\) is irrational.
विकल्पों में परिणाम की प्रकृति तय करने से पहले सरलीकरण करें। / In options, simplify first before deciding the nature of the result.
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Which of the following results is irrational?
A. \(\sqrt{2}+\sqrt{8}\)
\(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
\(3\sqrt{2}\) अपरिमेय है। / \(3\sqrt{2}\) is irrational.
विकल्पों में परिणाम निकालकर ही संख्या की प्रकृति तय करें। / In options, simplify the result before deciding its nature.
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Which statement is correct about \(\sqrt{2}+\sqrt{3}\)?
B. यह अपरिमेय हैIt is irrational
\(\sqrt{2}\) और \(\sqrt{3}\) दोनों अपरिमेय हैं। / Both \(\sqrt{2}\) and \(\sqrt{3}\) are irrational.
उनका योग \(\sqrt{5}\) नहीं होता; \(\sqrt{2}+\sqrt{3}\) अपरिमेय रहता है। / Their sum is not \(\sqrt{5}\); \(\sqrt{2}+\sqrt{3}\) remains irrational.
अलग-अलग वर्गमूलों को सीधे अंदर की संख्याएँ जोड़कर न लिखें। / Do not add the numbers inside different square roots directly.
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The simplified form of \(\sqrt{2}+\sqrt{2}\) is what type of number?
B. अपरिमेय संख्याIrrational number
\(\sqrt{2}+\sqrt{2}=2\sqrt{2}\)। / \(\sqrt{2}+\sqrt{2}=2\sqrt{2}\).
\(\sqrt{2}\) अपरिमेय है और (2) अशून्य परिमेय है, इसलिए \(2\sqrt{2}\) अपरिमेय है। / \(\sqrt{2}\) is irrational and (2) is non-zero rational, so \(2\sqrt{2}\) is irrational.
समान वर्गमूलों को पहले जोड़कर सरल करें। / First simplify like radicals, then decide the type.
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