Question 1/14
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प \(\sqrt{5}+\sqrt{20}+\sqrt{45}+\sqrt{80}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{5}+\sqrt{20}+\sqrt{45}+\sqrt{80}\)?
#surds
#addition
#like-terms
A \(12\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{150}\)
D \(6\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{5}\)
Step 1
Concept
The terms become \(\sqrt{5}+2\sqrt{5}+3\sqrt{5}+4\sqrt{5}\). The total is \(10\sqrt{5}\), so check the options carefully.
Step 2
Why this answer is correct
The correct answer is A. \(12\sqrt{5}\). The terms become \(\sqrt{5}+2\sqrt{5}+3\sqrt{5}+4\sqrt{5}\). The total is \(10\sqrt{5}\), so check the options carefully.
Step 3
Exam Tip
ये पद \(\sqrt{5}+2\sqrt{5}+3\sqrt{5}+4\sqrt{5}\) बनते हैं। कुल \(10\sqrt{5}\) नहीं बल्कि \(10\sqrt{5}\) है, विकल्पों को ध्यान से जाँचें।
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Question 2/14
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प \(4\sqrt{7}+2\sqrt{28}-\sqrt{175}\) का सरल रूप है?
Which option is the simplified form of \(4\sqrt{7}+2\sqrt{28}-\sqrt{175}\)?
#surds
#simplification
#like-terms
A \(3\sqrt{7}\)
B \(7\sqrt{7}\)
C \(\sqrt{84}\)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{175}=5\sqrt{7}\). Thus \(4\sqrt{7}+4\sqrt{7}-5\sqrt{7}=3\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{7}\). \(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{175}=5\sqrt{7}\). Thus \(4\sqrt{7}+4\sqrt{7}-5\sqrt{7}=3\sqrt{7}\).
Step 3
Exam Tip
\(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{175}=5\sqrt{7}\) है। इसलिए \(4\sqrt{7}+4\sqrt{7}-5\sqrt{7}=3\sqrt{7}\) है।
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Question 3/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(\sqrt{3}+\sqrt{27}+\sqrt{75}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{3}+\sqrt{27}+\sqrt{75}\)?
#surds
#addition
#like-terms
A \(9\sqrt{3}\)
B \(6\sqrt{3}\)
C \(\sqrt{105}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\). The total is \(9\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(9\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\). The total is \(9\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। कुल \(9\sqrt{3}\) मिलता है।
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Question 4/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(6\sqrt{3}-2\sqrt{3}+\sqrt{3}\) का सरल रूप है?
Which option is the simplified form of \(6\sqrt{3}-2\sqrt{3}+\sqrt{3}\)?
#surds
#like-terms
#simplification
A \(5\sqrt{3}\)
B \(9\sqrt{3}\)
C \(5\sqrt{9}\)
D \(\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
The coefficients of like radical terms are (6-2+1=5). So the answer is \(5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). The coefficients of like radical terms are (6-2+1=5). So the answer is \(5\sqrt{3}\).
Step 3
Exam Tip
समान जड़ वाले पदों के गुणांक (6-2+1=5) बनते हैं। इसलिए उत्तर \(5\sqrt{3}\) है।
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Question 5/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(\sqrt{7}+\sqrt{63}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{7}+\sqrt{63}\)?
#surds
#addition
#like-terms
A \(4\sqrt{7}\)
B \(10\sqrt{7}\)
C \(\sqrt{70}\)
D \(3\sqrt{14}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}\)
Step 1
Concept
\(\sqrt{63}=3\sqrt{7}\), so the sum is \(4\sqrt{7}\). Simplify roots first and then add like terms.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{7}\). \(\sqrt{63}=3\sqrt{7}\), so the sum is \(4\sqrt{7}\). Simplify roots first and then add like terms.
Step 3
Exam Tip
\(\sqrt{63}=3\sqrt{7}\) है इसलिए योग \(4\sqrt{7}\) है। पहले जड़ सरल करें फिर समान पद जोड़ें।
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Question 6/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\) का सरल रूप है?
Which option is the simplified form of \(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\)?
#surds
#like-terms
#simplification
A \(7\sqrt{2}\)
B \(8\sqrt{2}\)
C \(7\sqrt{6}\)
D \(\sqrt{14}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
The coefficients of like radical terms add as (5+3-1=7). So the answer is \(7\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). The coefficients of like radical terms add as (5+3-1=7). So the answer is \(7\sqrt{2}\).
Step 3
Exam Tip
समान जड़ वाले पदों के गुणांक (5+3-1=7) जुड़ते हैं। इसलिए उत्तर \(7\sqrt{2}\) है।
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Question 7/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(\sqrt{125}+\sqrt{45}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{125}+\sqrt{45}\)?
#surds
#addition
#like-terms
A \(8\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{170}\)
D \(6\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{5}\)
Step 1
Concept
\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{5}\). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। समान पद जोड़ने पर \(8\sqrt{5}\) मिलता है।
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Question 8/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प \(4\sqrt{3}-\sqrt{27}\) का मान है?
Which option is the value of \(4\sqrt{3}-\sqrt{27}\)?
#surds
#subtraction
#like-terms
A \(\sqrt{3}\)
B \(7\sqrt{3}\)
C \(\sqrt{24}\)
D (3)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) है। इसलिए \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\) होगा।
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Question 9/14
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{2}+\sqrt{8}+\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{2}+\sqrt{8}+\sqrt{18}\)?
#surds
#addition
#like-terms
A \(6\sqrt{2}\)
B \(11\sqrt{2}\)
C \(\sqrt{28}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\) है। कुल \(6\sqrt{2}\) मिलता है।
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Question 10/14
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(7\sqrt{3}+2\sqrt{3}\) का सही सरल रूप है?
Which option is the correct simplified form of \(7\sqrt{3}+2\sqrt{3}\)?
#surds
#like-terms
#addition
A \(9\sqrt{3}\)
B \(14\sqrt{3}\)
C \(9\sqrt{6}\)
D \(\sqrt{30}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{3}\)
Step 1
Concept
The coefficients of like radical terms are added. So \(7\sqrt{3}+2\sqrt{3}=9\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(9\sqrt{3}\). The coefficients of like radical terms are added. So \(7\sqrt{3}+2\sqrt{3}=9\sqrt{3}\).
Step 3
Exam Tip
समान जड़ वाले पदों के गुणांक जुड़ते हैं। इसलिए \(7\sqrt{3}+2\sqrt{3}=9\sqrt{3}\) है।
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Question 11/14
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
\(\sqrt{3}+\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{3}+\sqrt{75}\)?
#surds
#like-terms
#addition
A \(6\sqrt{3}\)
B \(5\sqrt{3}\)
C \(\sqrt{78}\)
D \(25\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), so the total is \(6\sqrt{3}\). Only like radical terms add directly.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). \(\sqrt{75}=5\sqrt{3}\), so the total is \(6\sqrt{3}\). Only like radical terms add directly.
Step 3
Exam Tip
\(\sqrt{75}=5\sqrt{3}\) इसलिए कुल \(6\sqrt{3}\) है। समान जड़ वाले पद ही सीधे जुड़ते हैं।
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Question 12/14
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
\(\sqrt{63}+\sqrt{28}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{63}+\sqrt{28}\)?
#surds
#addition
#like-terms
A \(5\sqrt{7}\)
B \(7\sqrt{5}\)
C \(\sqrt{91}\)
D \(11\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{7}\)
Step 1
Concept
\(\sqrt{63}=3\sqrt{7}\) and \(\sqrt{28}=2\sqrt{7}\). Adding like terms gives \(5\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{7}\). \(\sqrt{63}=3\sqrt{7}\) and \(\sqrt{28}=2\sqrt{7}\). Adding like terms gives \(5\sqrt{7}\).
Step 3
Exam Tip
\(\sqrt{63}=3\sqrt{7}\) और \(\sqrt{28}=2\sqrt{7}\) है। समान पद जोड़ने पर \(5\sqrt{7}\) मिलता है।
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Question 13/14
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
\(\sqrt{48}+\sqrt{12}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{48}+\sqrt{12}\)?
#surds
#addition
#like-terms
A \(6\sqrt{3}\)
B \(4\sqrt{15}\)
C \(60\sqrt{3}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{48}=4\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Adding like terms gives \(6\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). \(\sqrt{48}=4\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Adding like terms gives \(6\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{48}=4\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। समान पद जोड़ने पर \(6\sqrt{3}\) मिलता है।
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Question 14/14
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
\(\sqrt{2}+\sqrt{8}\) का सही सरल रूप क्या है?
What is the correct simplified form of \(\sqrt{2}+\sqrt{8}\)?
#surds
#addition
#like-terms
A \(3\sqrt{2}\)
B \(\sqrt{10}\)
C \(2\sqrt{10}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) so the sum is \(3\sqrt{2}\). Simplify first and then add like terms.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) so the sum is \(3\sqrt{2}\). Simplify first and then add like terms.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) इसलिए योग \(3\sqrt{2}\) है। पहले सरल करें फिर समान पद जोड़ें।
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