\( \sqrt{11}\approx3.316\), so \(p\approx-3.316\), which is less than (-3). Be careful with direction while comparing negatives.
Step 2
Why this answer is correct
The correct answer is A. (p<q). \( \sqrt{11}\approx3.316\), so \(p\approx-3.316\), which is less than (-3). Be careful with direction while comparing negatives.
Step 3
Exam Tip
\( \sqrt{11}\approx3.316\), इसलिए \(p\approx-3.316\) और यह (-3) से छोटा है। ऋणात्मक संख्याओं की तुलना में दिशा का ध्यान रखें।
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 2
Why this answer is correct
The correct answer is A. ((-3,-2)). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\) (2) और (3) के बीच है और ऋणात्मक मान (-3) और (-2) के बीच होगा। ऋणात्मक दिशा में क्रम उलट जाता है।
\(\sqrt{6}\approx2.45\), so \(-\sqrt{6}\approx-2.45\), which is left of (-2). The smaller number lies to the left.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{6}\). \(\sqrt{6}\approx2.45\), so \(-\sqrt{6}\approx-2.45\), which is left of (-2). The smaller number lies to the left.
Step 3
Exam Tip
\(\sqrt{6}\approx2.45\), इसलिए \(-\sqrt{6}\approx-2.45\) है जो (-2) से बाईं ओर है। छोटी संख्या बाईं ओर होती है।
Since \(\sqrt{7}\) lies between (2) and (3), \(-\sqrt{7}\) lies between (-3) and (-2). In exams, note the direction of a negative square root.
Step 2
Why this answer is correct
The correct answer is B. (-3) और (-2) / (-3) and (-2). Since \(\sqrt{7}\) lies between (2) and (3), \(-\sqrt{7}\) lies between (-3) and (-2). In exams, note the direction of a negative square root.
Step 3
Exam Tip
क्योंकि \(\sqrt{7}\) (2) और (3) के बीच है, इसलिए \(-\sqrt{7}\) (-3) और (-2) के बीच होगा। परीक्षा में ऋणात्मक वर्गमूल की दिशा ध्यान रखें।
\(-\sqrt{3}\) is negative, so it lies to the left of (0). Negative numbers are placed on the left side of the number line.
Step 2
Why this answer is correct
The correct answer is A. (0) के बाईं ओर / left of (0). \(-\sqrt{3}\) is negative, so it lies to the left of (0). Negative numbers are placed on the left side of the number line.
Step 3
Exam Tip
\(-\sqrt{3}\) ऋणात्मक संख्या है, इसलिए यह (0) के बाईं ओर होगी। ऋणात्मक संख्याएँ संख्या रेखा पर बाईं तरफ होती हैं।
\(\sqrt{59}\) is irrational because (59) is not a perfect square. Its negative is also a real irrational number.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. \(\sqrt{59}\) is irrational because (59) is not a perfect square. Its negative is also a real irrational number.
Step 3
Exam Tip
\(\sqrt{59}\) अपरिमेय है क्योंकि (59) पूर्ण वर्ग नहीं है। उसका ऋण भी वास्तविक अपरिमेय है।
\(\sqrt{47}\) is irrational because (47) is not a perfect square. Its negative is also a real irrational number.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. \(\sqrt{47}\) is irrational because (47) is not a perfect square. Its negative is also a real irrational number.
Step 3
Exam Tip
\(\sqrt{47}\) अपरिमेय है क्योंकि (47) पूर्ण वर्ग नहीं है। उसका ऋण भी वास्तविक अपरिमेय है।
\(\sqrt{13}\) is irrational and its negative is also irrational. The negative sign does not change realness.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. \(\sqrt{13}\) is irrational and its negative is also irrational. The negative sign does not change realness.
Step 3
Exam Tip
\(\sqrt{13}\) अपरिमेय है और उसका ऋण भी अपरिमेय है। ऋण चिह्न वास्तविकता को नहीं बदलता।
\(\sqrt{18}\) is irrational and its negative is also real irrational. A negative sign does not change rationality.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{18}\). \(\sqrt{18}\) is irrational and its negative is also real irrational. A negative sign does not change rationality.
Step 3
Exam Tip
\(\sqrt{18}\) अपरिमेय है और उसका ऋण भी वास्तविक अपरिमेय है। ऋण चिह्न परिमेयता नहीं बदलता।
\(\sqrt{7}\) is irrational and its negative is also irrational. The negative sign does not stop it from being real.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. \(\sqrt{7}\) is irrational and its negative is also irrational. The negative sign does not stop it from being real.
Step 3
Exam Tip
\(\sqrt{7}\) अपरिमेय है और उसका ऋण भी अपरिमेय होता है। ऋण चिह्न संख्या को वास्तविक होने से नहीं रोकता।
A negative sign changes direction, not rationality.
Step 2
Why this answer is correct
If (-x) were rational, then (x) would also be rational, which is false.
Step 3
Exam Tip
Treat the sign of a number and its type separately. चरण 1: ऋण चिह्न केवल संख्या की दिशा बदलता है, उसकी परिमेयता नहीं। चरण 2: यदि (-x) परिमेय हो, तो (x) भी परिमेय होगा, जो गलत है। चरण 3: संख्या के चिह्न और संख्या की प्रकृति को अलग-अलग समझें।
