square-root-spiral se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
650 questions tagged with square-root-spiral.
In a square root spiral, the length \(\sqrt{5}\) lies between which whole numbers?
B. (2) और (3)(2) and (3)
क्योंकि \(2^2<5<3^2\) है। इसलिए \(2<\sqrt{5}<3\) होता है। / Because \(2^2<5<3^2\). Therefore \(2<\sqrt{5}<3\).
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In a square root spiral, the length \(\sqrt{3}\) lies between which whole numbers?
B. (1) और (2)(1) and (2)
क्योंकि \(1^2<3<2^2\) है। इसलिए \(1<\sqrt{3}<2\) होता है। / Because \(1^2<3<2^2\). Therefore \(1<\sqrt{3}<2\).
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Why is the length \(\sqrt{2}\) placed between (1) and (2) in a square root spiral?
A. क्योंकि \(1^2<2<2^2\)Because \(1^2<2<2^2\)
\(1^2<2<2^2\) से \(1<\sqrt{2}<2\) मिलता है। संख्या रेखा पर स्थान इसी से समझ आता है। / From \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). This helps locate it on the number line.
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C. \(\sqrt{7}\)
नया कर्ण \(\sqrt{6+1}=\sqrt{7}\) होगा। यह पाइथागोरस प्रमेय से मिलता है। / The new hypotenuse is \(\sqrt{6+1}=\sqrt{7}\). This follows from Pythagoras theorem.
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In a square root spiral, if the new hypotenuse is \(\sqrt{n+1}\), what was the previous hypotenuse?
A. \(\sqrt{n}\)
नया कर्ण पिछले \(\sqrt{n}\) और (1) इकाई लंब से बनता है। इसलिए पिछला कर्ण \(\sqrt{n}\) था। / The new hypotenuse is formed from previous \(\sqrt{n}\) and a (1) unit perpendicular. Therefore the previous hypotenuse was \(\sqrt{n}\).
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In a square root spiral, which theorem allows writing \(\sqrt{1^2+1^2}\) to make \(\sqrt{2}\)?
A. पाइथागोरस प्रमेयPythagoras theorem
समकोण त्रिभुज में कर्ण के लिए पाइथागोरस प्रमेय लगता है। इसलिए \(\sqrt{1^2+1^2}=\sqrt{2}\) मिलता है। / Pythagoras theorem is used for the hypotenuse in a right triangle. Thus \(\sqrt{1^2+1^2}=\sqrt{2}\).
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What is the main geometric benefit of a square root spiral?
A. वर्गमूल लंबाइयों का निर्माण करनाTo construct square root lengths
वर्गमूल सर्पिल \(\sqrt{2},\sqrt{3},\sqrt{4}\) जैसी लंबाइयाँ ज्यामितीय रूप से बनाता है। यह संख्या रेखा पर भी उपयोगी है। / A square root spiral geometrically constructs lengths like \(\sqrt{2},\sqrt{3},\sqrt{4}\). It is also useful on the number line.
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Just before making \(\sqrt{15}\) in a square root spiral, which length will have already been made?
B. \(\sqrt{14}\)
\(\sqrt{14}\) पिछले चरण का कर्ण होगा। उसमें (1) इकाई लंब जोड़कर \(\sqrt{15}\) बनेगा। / \(\sqrt{14}\) will be the previous hypotenuse. Adding a (1) unit perpendicular to it gives \(\sqrt{15}\).
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In a square root spiral, which hypotenuse comes after \(\sqrt{24}\)?
C. \(\sqrt{25}\)
हर अगले चरण में संख्या (1) बढ़ती है। इसलिए \(\sqrt{24}\) के बाद \(\sqrt{25}\) आता है। / At each next step, the number increases by (1). Therefore \(\sqrt{25}\) comes after \(\sqrt{24}\).
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Which relation between \(\sqrt{2}\) and \(\sqrt{3}\) is correct in a square root spiral?
A. \(\sqrt{3}\) अगला कर्ण है\(\sqrt{3}\) is the next hypotenuse
\(\sqrt{2}\) के बाद (1) इकाई लंब जोड़ने से \(\sqrt{3}\) बनता है। क्रम को ध्यान रखें। / After \(\sqrt{2}\), adding a (1) unit perpendicular forms \(\sqrt{3}\). Keep the order in mind.
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Which statement is incorrect for a square root spiral?
D. हर कर्ण हमेशा पूर्ण संख्या होता हैEvery hypotenuse is always a whole number
\(\sqrt{2},\sqrt{3},\sqrt{5}\) जैसे कई कर्ण पूर्ण संख्या नहीं होते। इसलिए यह कथन गलत है। / Many hypotenuses like \(\sqrt{2},\sqrt{3},\sqrt{5}\) are not whole numbers. So this statement is incorrect.
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B. \(\sqrt{20}\) का कर्णHypotenuse of \(\sqrt{20}\)
जिस वर्गमूल को संख्या रेखा पर रखना है, उसी कर्ण की लंबाई कंपास में ली जाती है। / The hypotenuse length of the required square root is taken in the compass to place it on the number line.
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B. \(\sqrt{17}\)
\(\sqrt{17}\) के साथ (1) इकाई लंब से \(\sqrt{18}\) बनता है। पिछली संख्या हमेशा (1) कम होती है। / With \(\sqrt{17}\) and a (1) unit perpendicular, \(\sqrt{18}\) is formed. The previous number is always (1) less.
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In a square root spiral, which hypotenuse will be formed after \(\sqrt{12}\)?
C. \(\sqrt{13}\)
नया कर्ण \(\sqrt{12+1}=\sqrt{13}\) होता है। क्रम में अगला वर्गमूल लें। / The new hypotenuse is \(\sqrt{12+1}=\sqrt{13}\). Take the next square root in sequence.
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In a square root spiral, a length like \(\sqrt{25}\) gives which type of number?
A. पूर्ण संख्याWhole number
\(\sqrt{25}=5\) होता है। पूर्ण वर्गों के वर्गमूल पूर्ण संख्या देते हैं। / \(\sqrt{25}=5\). Square roots of perfect squares give whole numbers.
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After making \(\sqrt{4}\) in a square root spiral, which next irrational length can be obtained?
A. \(\sqrt{5}\)
\(\sqrt{4}=2\) परिमेय है। अगला कर्ण \(\sqrt{5}\) होगा, जो अपरिमेय है। / \(\sqrt{4}=2\) is rational. The next hypotenuse is \(\sqrt{5}\), which is irrational.
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In a square root spiral, which two sides form the right angle to make \(\sqrt{3}\)?
A. \(\sqrt{2}\) और (1)\(\sqrt{2}\) and (1)
\(\sqrt{2}\) पिछला कर्ण है और (1) इकाई नई लंब है। इनसे नया कर्ण \(\sqrt{3}\) बनता है। / \(\sqrt{2}\) is the previous hypotenuse and (1) unit is the new perpendicular. Together they form new hypotenuse \(\sqrt{3}\).
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In a square root spiral, length \(\sqrt{2}\) is obtained from a right triangle with which two sides?
A. (1) इकाई और (1) इकाई(1) unit and (1) unit
(1) और (1) इकाई भुजाओं से कर्ण \(\sqrt{2}\) मिलता है। यह सर्पिल का पहला मुख्य चरण है। / Sides (1) and (1) units give hypotenuse \(\sqrt{2}\). This is the first main step of the spiral.
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What is the purpose of adding a (1) unit perpendicular in a square root spiral?
A. अगला वर्गमूल कर्ण बनानाTo make the next square root as hypotenuse
(1) इकाई लंब जोड़ने से नया समकोण त्रिभुज बनता है। उसका कर्ण अगला वर्गमूल देता है। / Adding a (1) unit perpendicular forms a new right triangle. Its hypotenuse gives the next square root.
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A. \(\sqrt{n+1}\)
नया कर्ण (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) होता है। यह वर्गमूल सर्पिल का नियम है। / The new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the rule of the square root spiral.
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In a square root spiral, what will be the next hypotenuse after \(\sqrt{14}\)?
C. \(\sqrt{15}\)
हर नए चरण में संख्या (1) बढ़ती है। इसलिए \(\sqrt{14}\) के बाद \(\sqrt{15}\) आता है। / At each new step, the number increases by (1). Therefore \(\sqrt{15}\) comes after \(\sqrt{14}\).
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Just before making \(\sqrt{13}\) in a square root spiral, which hypotenuse should be present?
B. \(\sqrt{12}\)
\(\sqrt{12}\) में (1) इकाई लंब जोड़ने पर नया कर्ण \(\sqrt{13}\) बनता है। पिछला कर्ण एक कम संख्या का होता है। / Adding a (1) unit perpendicular to \(\sqrt{12}\) forms \(\sqrt{13}\). The previous hypotenuse has one less number.
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In a square root spiral, the length \(\sqrt{1}\) is equal to what?
B. (1)
\(\sqrt{1}=1\) होता है। यही प्रारंभिक (1) इकाई रेखाखंड है। / \(\sqrt{1}=1\). This is the initial (1) unit line segment.
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The lines formed in a square root spiral gradually look like which shape?
A. सर्पिलSpiral
लगातार बने समकोण त्रिभुज मुड़ते हुए सर्पिल जैसी आकृति बनाते हैं। इसलिए इसे वर्गमूल सर्पिल कहते हैं। / Successive right triangles turn around and make a spiral-like shape. Hence it is called a square root spiral.
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Which calculation is used when \(\sqrt{3}\) becomes \(\sqrt{4}\) in a square root spiral?
A. (\(\sqrt{3}\)2+12=4)
\(\sqrt{3}\) और (1) इकाई से नया कर्ण \(\sqrt{4}\) मिलता है। सही गणना वर्गों के योग से होती है। / With \(\sqrt{3}\) and (1) unit, the new hypotenuse is \(\sqrt{4}\). The correct calculation uses sum of squares.
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What is the reason for \(\sqrt{2}\) becoming \(\sqrt{3}\) in a square root spiral?
A. (\(\sqrt{2}\)2+12=3)
पाइथागोरस प्रमेय से नया कर्ण \(\sqrt{2+1}=\sqrt{3}\) बनता है। \(\sqrt{2}+1\) को \(\sqrt{3}\) न मानें। / By Pythagoras theorem, the new hypotenuse becomes \(\sqrt{2+1}=\sqrt{3}\). Do not treat \(\sqrt{2}+1\) as \(\sqrt{3}\).
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A. कंपासCompass
कंपास से कर्ण की लंबाई लेकर संख्या रेखा पर चाप लगाया जाता है। यही ज्यामितीय निर्माण है। / With a compass, the hypotenuse length is taken and an arc is drawn on the number line. This is the geometric construction.
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To make \(\sqrt{11}\) in a square root spiral, what should be the previous hypotenuse length?
B. \(\sqrt{10}\)
\(\sqrt{10}\) के साथ (1) इकाई लंब जोड़ने पर \(\sqrt{11}\) बनता है। क्रमिक निर्माण याद रखें। / Adding a (1) unit perpendicular to \(\sqrt{10}\) forms \(\sqrt{11}\). Remember the stepwise construction.
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In a square root spiral, the length \(\sqrt{16}\) will be equal to which number?
C. (4)
\(\sqrt{16}=4\) होता है। पूर्ण वर्गों के वर्गमूल परिमेय और पूर्ण संख्या होते हैं। / \(\sqrt{16}=4\). Square roots of perfect squares are rational and whole numbers.
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In a square root spiral, \(\sqrt{5}\) is an example of which type of number?
B. अपरिमेय संख्याIrrational number
\(\sqrt{5}\) पूर्ण वर्ग का वर्गमूल नहीं है। इसलिए यह अपरिमेय संख्या है। / \(\sqrt{5}\) is not the square root of a perfect square. Therefore it is irrational.
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