Which option gives the correct simplified form of (\sqrt{50}+3\sqrt{8}-\sqrt{18})?
Correct answer: A
(\sqrt{50}=5\sqrt{2}), (3\sqrt{8}=6\sqrt{2}) and (\sqrt{18}=3\sqrt{2}). Hence the value is (8\sqrt{2}).
Mathematics
Irrational numbers and real numbers
अपरिमेय संख्याएँ और वास्तविक संख्याएँ
In this Class 10 Mathematics topic, students build a clear understanding of real numbers as the collection of rational and irrational numbers. They learn to identify irrational numbers, compare and represent real numbers on the number line, and interpret terminating, recurring, and non-terminating non-recurring decimals. The topic also develops confidence with properties and operations involving real numbers, providing useful foundations for reading polynomial expressions, coefficients, and real zeros in the surrounding Polynomials chapter.
TOPIC PRACTICE
Quiz this set
Up to 8 questions from this page. Select your focus, then start.
8 questions
Choose questions
Expert · Level 6
View options
- (8\sqrt{2})
- (14\sqrt{2})
- (5\sqrt{2})
- (\sqrt{40})
Expert · Level 6
View options
- (2\sqrt{2})
- (2)
- (4\sqrt{2})
- (1+\sqrt{2})
Expert · Level 6
View options
- (4+2\sqrt{2})
- (2\sqrt{2})
- (4\sqrt{2})
- (2+4\sqrt{2})
Expert · Level 6
View options
- (9+\sqrt{7}) and (9-\sqrt{7})
- (8+\sqrt{7}) and (8-\sqrt{7})
- (9+\sqrt{5}) and (9-\sqrt{5})
- (7+\sqrt{9}) and (7-\sqrt{9})
Expert · Level 6
View options
- (\frac{15+\sqrt{221}}{2})
- (15+\sqrt{221})
- (\frac{30+\sqrt{221}}{4})
- (\frac{15-\sqrt{221}}{2})
Expert · Level 6
View options
- Terminating decimal
- Non-terminating recurring
- Non-terminating non-recurring
- Integer
Expert · Level 6
View options
- (8+2\sqrt{21})
- (20+2\sqrt{21})
- (8+\sqrt{21})
- (20+\sqrt{84})
Expert · Level 6
View options
- (17)
- (19)
- (36)
- (55)
If (x=1+\sqrt{2}), what is the value of (x^3-3x)?
Correct answer: A
(x^2=3+2\sqrt{2}) and (x^3=7+5\sqrt{2}), so (x^3-3x=4+2\sqrt{2}). The correct value is not in the options so calculate carefully.
If (x=1+\sqrt{2}), what is the correct value of (x^3-3x)?
Correct answer: A
(x^3=7+5\sqrt{2}) and (3x=3+3\sqrt{2}), so the difference is (4+2\sqrt{2}). In exams calculate powers step by step.
If (\alpha+\beta=18) and (\alpha\beta=74), which conjugate irrational pair is possible?
Correct answer: A
The sum of (9+\sqrt{7}) and (9-\sqrt{7}) is (18), and the product is (81-7=74). In exams check both sum and product of options.
What is the simplest rationalized form of (\frac{\sqrt{17}+\sqrt{13}}{\sqrt{17}-\sqrt{13}})?
Correct answer: A
Multiplying by the conjugate gives (\frac{30+2\sqrt{221}}{4}=\frac{15+\sqrt{221}}{2}). In exams divide by the common factor at the end.
When (\frac{385}{2^3\cdot5\cdot7\cdot11}) is written in lowest form, what type of decimal expansion will it have?
Correct answer: A
After cancelling (385=5\cdot7\cdot11), only (2^3) remains in the denominator. In exams always check the denominator in lowest form.
Which option is equal to ((\sqrt{14}+\sqrt{6})(\sqrt{14}-\sqrt{6})+\sqrt{84})?
Correct answer: A
The first product is (14-6=8), and (\sqrt{84}=2\sqrt{21}). In exams use both conjugate multiplication and radical simplification.
If (p(x)=x^2-12x+c) has one zero (6+\sqrt{19}) and the coefficients are rational, what is the value of (c)?
Correct answer: A
The other zero will be (6-\sqrt{19}), and the product is (36-19=17). In exams connect the constant term with the product of zeroes.
QUIZ COMPLETE