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Which of the following is not a rational number?
is not a rational number because 3 is not a perfect square, whereas 4, 25 and 36 are perfect square numbers and their square root is a rational number.
What type of number is \( (\sqrt{3}+\sqrt{5})^{2} \)?
(1)
The result obtained after solving the given expression is in which 8 is a rational number and
is an irrational number. So the given number is an irrational number.
What is the rationalizing factor of \( \sqrt[4]{pq^{2}r^{3}} \)?
Rationalizing factor of . Therefore, the rationalizing factor of
.
What is the product of \( \sqrt[3]{25} \) and \( \sqrt[3]{35} \)?
(1)
What is the value of \( p-q^{p-q} \) if \( p=3 \) and \( q=-3 \)?
(1)
What is the value of \( x \) if \( 8^{x+2} = 4160-8^{x} \)?
(1)
What is the value of \( x+\frac{1}{x} \) if \(x=2-\sqrt{3}\)?
(1)
What is the value of \( \frac{1}{x^{2}}+\frac{1}{y^{2}}\) if \(x=8+3\sqrt{7}\) and \(xy=1 \)?
(1)
What is the value of \( x^{3}-4x^{2}-x+10 \) if \(x=\frac{1}{\sqrt{5}-2}\)?
(1)
What is the value of \( p^{p}+q^{q} \) if \(p=2\) and \(q=5\)?
(1)
Which of the following is the simplest form of \( \frac{5\sqrt{2}+2\sqrt{5}}{5\sqrt{2}-2\sqrt{5}}\)?
(1)
If \( p\) and \( q \) are integers and it is given that \( \sqrt{pq} = 6\), then which of the following can’t be the value of \( p+q \)?
(1)
Possible values of Therefore, out of the given options 11 cannot be equal to
.
If \( x= \sqrt[3]{\sqrt{6}-\sqrt{5}}\) then what is the value of \( x^{3}+\frac{1}{x^{3}} \)?
(1)
Which of the following symbol is used to represent the set of all positive integers?
All the positive integers are basically Natural numbers. Therefore, the symbol N is used to represent them.
If \( a+b\sqrt{5} = \frac{\sqrt{5}+1}{\sqrt{5}-2} \) then what is the value of \( ab \)?
(1)
If \( \frac{a}{b}+\frac{b}{a} = 1 \) then what is the value of \( a^{3}+b^{3} \)?
(1)
What is the positive square root of \( 8+2\sqrt{7} \)?
(1)
Comparing the equation, we get and
. Therefore,
. The square root of
.
What is the value of \( x \) in the equation \( \frac{5^{5x} \times 25^{2} \times 15625}{5^{3x}} = 5^{8} \)?
(1)
What is the value of \( x \) if \( 5^{3x-4} \cdot 7^{x+1} = 8575 \)?
(1)
Comparing both the sides, we get
(2)
and
(3)
Therefore,
What is the value of \( \frac{1}{\sqrt{10}-3} – \frac{1}{3-\sqrt{8}} + \frac{1}{\sqrt{8}-\sqrt{7}} \)?
(1)