Sample QuestionsRationalisation [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following is the value of $(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})$ ?
- ✓
- B
- C
$\sqrt{7}$
- D
$\sqrt{11}$
Answer: A.
View full solution →The value of $\sqrt{5-2 \sqrt{6}}$ is
- ✓
$\sqrt{3}-\sqrt{2}$
- B
$\sqrt{2}-\sqrt{3}$
- C
$\sqrt{5}-\sqrt{6}$
- D
$\sqrt{5}+\sqrt{6}$
Answer: A.
View full solution →The value of $\sqrt{5+2 \sqrt{6}}$, is
- A
$\sqrt{3}-\sqrt{2}$
- ✓
$\sqrt{3}+\sqrt{2}$
- C
$\sqrt{5}+\sqrt{6}$
- D
Answer: B.
View full solution →The value of $\sqrt{3-2 \sqrt{2}}$, is
- ✓
$\sqrt{2}-1$
- B
$\sqrt{2}+1$
- C
$\sqrt{3}-\sqrt{2}$
- D
$\sqrt{3}+\sqrt{2}$
Answer: A.
View full solution →The value of $\sqrt{20} \times\sqrt{5}$ is
- ✓
- B
$2 \sqrt{5}$
- C
$20 \sqrt{5}$
- D
$4 \sqrt{5}$
Answer: A.
View full solution →The number obtained by rationalising the denominator of $\frac{1}{\sqrt{7}+2}$ is _______________ .
View full solution →$\sqrt{7+2 \sqrt{6}}-\sqrt{7-2 \sqrt{6}}=$ _______________ .
View full solution →If $x=\sqrt{6}+\sqrt{5}$, then $x^2+\frac{1}{x^2}-2=$ _______________ .
View full solution →If $x=\frac{2}{\sqrt{3}-\sqrt{5}}$ and $y=\frac{2}{\sqrt{3}+\sqrt{5}}$, then $x+y=$ _______________ .
View full solution →If $x=\frac{2}{\sqrt{10}-\sqrt{8}}$ and $y=\frac{2}{\sqrt{10}+2 \sqrt{2}}$, then $(x-y)^2=$
View full solution →Write the value of $(2+\sqrt{3})(2-\sqrt{3})$.
View full solution →Write the reciprocal of $5+\sqrt{2}$.
View full solution →Write the rationalisation factor of $\sqrt{5}-2$.
View full solution →Write the rationalisation factor of $7-3 \sqrt{5}$.
View full solution →Simplify: $\sqrt{3-2 \sqrt{2}}$.
View full solution →Write the value of $\big(2+\sqrt3)(2-\sqrt3\big).$
View full solution →Write the reciprocal $5+\sqrt2.$
View full solution →Write the rationalisation factor of $\sqrt5-2.$
View full solution →Write the rationalisation factor of $7-3\sqrt5.$
View full solution →Simplify the following: $\sqrt[3]{4}\times\sqrt[3]{16}$
View full solution →Simplify:
$\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}+\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}$
View full solution →Simplify:
$\frac{3\sqrt2-2\sqrt3}{3\sqrt2+2\sqrt3}+\frac{\sqrt{12}}{\sqrt3-\sqrt2}$
View full solution →Simplify:
$\frac{2}{\sqrt5+\sqrt3}+\frac{1}{\sqrt3+\sqrt2}-\frac{3}{\sqrt5+\sqrt2}$
View full solution →Simplify:
$\frac{1}{2+\sqrt3}+\frac{2}{\sqrt5-\sqrt3}+\frac{1}{2-\sqrt5}$
View full solution →Rationales the denominator and simplify:
$\frac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}$
View full solution →Simplify:
$\frac{7+3\sqrt5}{3+\sqrt5}-\frac{7-3\sqrt5}{3-\sqrt5}$
View full solution →If $\text{x}=\frac{\sqrt3+1}{2},$ find the value of $4\text{x}^3+2\text{x}^2-8\text{x}+7.$
View full solution →If $\text{x}=3+\sqrt8,$ find the value of $\text{x}^2+\frac{1}{\text{x}^2}.$
View full solution →If $\text{x}=2+\sqrt3,$ find the value of $\text{x}+\frac{1}{\text{x}}.$
View full solution →If $\text{x}=2+\sqrt3,$ find the value of $\text{x}^3+\frac{1}{\text{x}^3}.$
View full solution →Mr. Roy, a Mathematics teacher explained some key points of unit 1 of class IX to his students. Some are given here.
• There are infinite rational numbers between any two rational numbers.
• Rationalisation of a denominator means to change the irrational denominator to rational form.
• A number is irrational if its decimal form is non-terminating and non-recurring. On the basis of these key points, choose the correct option in the following questions:
(i) What is the reciprocal of $2+\sqrt{3}$ ?
(a) $\sqrt{3}+2$ $\quad$(b) $\frac{1}{\sqrt{3}-2}$$\quad$ (c) $2-\sqrt{3}$ $\quad$(d) $\frac{1}{2}+\frac{1}{\sqrt{3}}$
(ii) Which of the following is irrational?
(a) $\frac{\sqrt{4}}{\sqrt{9}}$$\quad$ (b) $\frac{\sqrt{12}}{\sqrt{3}}$ $\quad$(c) $\sqrt{7}$ $\quad$(d) $\sqrt{81}$
(iii) Which of the following is irrational?
(a) 0.14 $\quad$(b) $0.14 \overline{16}$ $\quad$(c) $0.1 \overline{416}$ $\quad$(d) 0.401400140001......
(iv) Which of the following is value of $(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})$ ?
(a) $\sqrt{11}$$\quad$ (b) 4 $\quad$(c) -4 $\quad$(d) $\sqrt{7}$
View full solution →