Value of (256)^{0.16}\times(256)^{0.09} is ______.
The value of 1.999… in the form p/q, where p and q are integers and q ≠ 0 , is
The number obtained on rationalizing the denominator of \frac{1}{\sqrt{7}-2} is _________.
The product \sqrt[3]{2}\cdot\sqrt[4]{2}\cdot\sqrt[12]{32} equals _________.
After rationalizing the denominator of \frac{7}{3\sqrt{3}-2\sqrt{2}}, we get the denominator as _______.
The value of \frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}} is equal to ________.
If \sqrt{2}=1.4142, then \sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}} is equal to _________.
\sqrt[4]{\sqrt[3]{2^2}} is equal to _______
Value of \sqrt[4]{(81)^{-2}} is ________.
Which of the following is equal to x?
The decimal expansion of the number √2 is __________.
Every rational number is _______
Between two rational numbers _____
Decimal representation of a rational number cannot be ___________
The product of any two irrational numbers is _____.
Which of the following is irrational?
\frac{1}{\sqrt{9}-\sqrt{8}} is equal to ________.
A rational number between √2 and √3 is ___________>
√10 x √15 is equal to _____
2√3 + √3 is equal to ______________
Every rational number is
(A) a natural number
(B) an integer
(C) a real number
(D) a whole number
Between two rational numbers
(A) there is no rational number
(B) there is exactly one rational number
(C) there are infinitely many rational numbers
(D) there are only rational numbers and no irrational numbers
Decimal representation of a rational number cannot be
(A) terminating
(B) non-terminating
(C) non-terminating repeating
(D) non-terminating non-repeating
The product of any two irrational numbers is
(A) always an irrational number
(B) always a rational number
(C) always an integer
(D) sometimes rational, sometimes irrational
The decimal expansion of the number √2 is
(A) a finite decimal
(B) 1.41421
(C) non-terminating recurring
(D) non-terminating non-recurring
(A) √4/√9
(B) √12/√3
(C) √7
(D) √81
A rational number between 2 and 3 is
(A) (√2+√3)/2
(B) (√2. √3)/2
(C) 1.5
(D) 1.8
(A) 19/10
(B) 1999/1000
(C) 2
(D) 1/9
2√3 + √3 is equal to
(A) 2√6
(B) 6
(C) 3√3
(D) 4√6
0.5918 is rational number.
\frac{\sqrt{12}}{\sqrt{75}} is rational number.
(1+\sqrt{5})-(4+\sqrt{5}) is a rational number.
Let x and y be rational and irrational numbers, respectively. x + y is an irrational number.
Let x be rational and y be irrational. xy is irrational number only.
\frac{\sqrt{2}}{3} is a rational number.
Number of rational numbers between 15 and 18 is finite.
The square of an irrational number is always rational.
There are infinitely many integers between any two integers.
1.010010001\dots is a rational number.
There are numbers that can be written in the form p/q, q≠0, and p, q both are not integers.
-\sqrt{0.4} is rational number.
\frac{\sqrt{12}}{\sqrt{3}} is not a rational number as √12 and √3 are not integers.
10.124124\dots is an irrational number.
\frac{\sqrt{15}}{\sqrt{3}} is written in the form p/q , where q ≠ 0, so it is a rational number.
\sqrt{196} is rational number.
\sqrt{\frac{9}{27}} is a rational number.
3\sqrt{18} is a rational number.
\frac{\sqrt{28}}{\sqrt{343}} is rational number.
Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.
Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.
Which is the rational number between 0 and 0.1?
Rationalize the denominator in \frac{4}{\sqrt{3}}. Evaluate by taking \sqrt{3}=1.732 up to three decimal places and select the correct option.
What is the value of a and b in \frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11} \sqrt{5} b?
If a=2+\sqrt{3}, then what is the value of a-\frac{1}{a}?
Rationalize the denominator in \frac{6}{\sqrt{6}}, take the value up to three decimal places and select the correct option.
Rationalize the denominator in \frac{\sqrt{10}-\sqrt{5}}{2} and hence evaluate by taking \sqrt{2}=1.414, \text { and } \sqrt{5}=2.236, upto three places of decimal.
Select the correct option.
Rationalize the denominator in \frac{\sqrt{2}}{2+\sqrt{2}} and hence evaluate by taking \sqrt{2}=1.414, upto three places of decimal.
Rationalize the denominator in \frac{1}{\sqrt{3}+\sqrt{2}} and hence evaluate by taking \sqrt{2}=1.414, \sqrt{3}=1.732, upto three places of decimal.
Rationalize the denominator of \frac{2}{3\sqrt{3}} and select the correct option.
Simplify 4 \sqrt{28} \div 3 \sqrt{7} and select the correct option.
Which is the rational number between √2 and √3?
Which is the rational number between -\frac{2}{5}\ and\ \frac{1}{2}?
Which is the rational number between –1 and –2?
Which is the rational number between 0.15 and 0.16?
Simplify
?2 =\frac{17}{4}
The valus of u is a rational number.
Which is the rational number between 2.357 and 3.121?
Which is the rational number between 6.375289 and 6.375738?
Which is the rational number between 2 and 3?
Simplify y2 = 9
The valus of y is a rational number.
Simplify x2 = 5
The valus of x is a rational number.
Simplify:
z2 = 0.04
The valus of z is an irrational number.
Which is the rational number between \frac{1}{3}\ and\ \frac{1}{2}?
Express 0.888… in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Which is the rational number between \frac{5}{7}\ and\ \frac{6}{7} ?
Which is the rational number between \frac{1}{4}\ and\ \frac{1}{5} ?
Which is the rational number between 0.1 and 0.11?
Which is the rational number between 0.00010 and 0.0012?
Express 0.2 in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Express 0.\overline{001} in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Express 5.2…. in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Express 0.2555… in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Express 0.1\overline{34} in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Express 0.00323232… in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Express 0.404040… in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
Simplify \sqrt{45}-3\sqrt{20}+4\sqrt{5} and select the correct option.
0.142857142857\ldots=\frac{1}{7}
Simplify 3 \sqrt{3}+2 \sqrt{27}+\frac{7}{\sqrt{3}} and select the correct option.
Rationalize the denominator of \frac{3+\sqrt{2}}{4 \sqrt{2}} and select the correct option.
Rationalize the denominator of \frac{16}{\sqrt{41}-5} and select the correct option.
Rationalize the denominator of \frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} and select the correct option.
Simplify \frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}} and select the correct option.
Simplify (\sqrt{3}-\sqrt{2})^{2} and select the correct option.
Simplify \frac{2\sqrt{3}}{3}-\frac{\sqrt{3}}{6} and select the correct option.
Simplify \sqrt[4]{81}-8 \sqrt[3]{216}+15 \sqrt[3]{32}+\sqrt{225} and select the correct option.
Rationalize the denominator of \frac{\sqrt{40}}{\sqrt{3}} and select the correct option.
Which is the rational number between 3.623623 and 0.484848?
Simplify \frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9} and select the correct option.
Rationalize the denominator of \frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}} and select the correct option.
Rationalize the denominator of \frac{2+\sqrt{3}}{2-\sqrt{3}} and select the correct option.
Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}} and select the correct option.
Rationalize the denominator of \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}} and select the correct option.
Simplify 4\sqrt{12}\times7\sqrt{6} and select the correct option.
What is the value of ‘a’ in \frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a-6\sqrt{3}?
What is the value of b in \frac{\sqrt{2}+\sqrt{3}}{3 \sqrt{2}-2 \sqrt{3}}=2-b \sqrt{6}?
What is the value of ‘a’ in \frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}?
Find which of the variables x, y, z and u represent rational numbers and which irrational
numbers:
(i) x² = 5
(ii) y² = 9
(iii) z² = .04
(iv) ?² = 17/4
Find three rational numbers between
(i) –1 and –2
(ii) 0.1 and 0.11
(iii) 5/7 and 6/7
(iv) 1/4 and 1/5
Insert a rational number and an irrational number between the following:
(i) 2 and 3
(ii) 0 and 0.1
(iii) 1/3 and 1/2
(iv) – 2/5 and 1/2
(v) 0.15 and 0.16
(vi) √2 and √3
(vii) 2.357 and 3.121
(viii) .0001 and .001
(ix) 3.623623 and 0.484848
(x) 6.375289 and 6.375738.
Represent the following numbers on the number line:
7, 7.2, −3/2 , −12/5
Locate √5, √10 and √17 on the number line.
Represent geometrically the following numbers on the number line:
(i) √4.5
(ii) √5.6
(iii) √8.1
(iv) √2.3
Express the following in the form p/q, where p and q are integers and q ≠ 0 :
(I) 0.2
(ii) 0.888…
(iii)
(iv)
(v) 0.2555…
(vi)
(vii) .00323232…
(viii) .404040…]
What is the value of \frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{3}}}?
Simplify (256)^{-\left(4\frac{3}{2}\right)} and select the correct option
If √2 =1.414, √3 =1.732, then what is the value of \frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}?
If a=\frac{3+\sqrt{5}}{2}, then what is the value of a^2+\frac{1}{a^2}?
Express 0.6+0.\overline{7}+0.4\overline{7} in the form p/q, where p and q are integers and q ≠ 0 and select the correct option.
If x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}},\text{ and }y=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}, then what is the value of x^2+y^2?
Simplify \frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}
Express 0.6+0 . \overline{7}+0.4 \overline{7} in the form p/q, where p and q are integers and q ≠ 0.
\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+5}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}
If √2 =1.414, √3 =1.732, then find the value of
\frac{4}{3 \sqrt{3}-2 \sqrt{2}}+\frac{3}{3 \sqrt{3}+2 \sqrt{2}}
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