Sample QuestionsRationalisation questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\sqrt2=1.414,$ then the value of $\sqrt6-\sqrt3$ upto three place of decimal is:
Answer: B.
View full solution →$\sqrt{10}\times\sqrt{15}$ is equal to:
- ✓
$5\sqrt6$
- B
$6\sqrt5$
- C
$\sqrt{30}$
- D
$\sqrt{25}$
Answer: A.
View full solution →If $\text{x}=7+4\sqrt3$ and $xy = 1$, then $\frac{1}{\text{x}^2}+\frac{1}{\text{y}^2}=$
- A
$64$
- B
$134$
- ✓
$194$
- D
$\frac{1}{49}$
Answer: C.
View full solution →If $\frac{\sqrt3-1}{\sqrt3+1}=\text{a}-\text{b}\sqrt3,$ then:
- ✓
$a = 2, b = 1$
- B
$a = 2, b = -1$
- C
$a = -2, b = 1$
- D
$a = b = 1$
Answer: A.
View full solution →If $\text{x}=\sqrt6+\sqrt5,$ then $\text{x}^2+\frac{1}{\text{x}^2}-2=$
- A
$2\sqrt6$
- B
$2\sqrt5$
- C
$24$
- ✓
$20$
Answer: D.
View full solution →If $\sqrt{13-x \sqrt{10}}=\sqrt{8}+\sqrt{5}$, then $x=$ _______________ .
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 →$\sqrt{7+2 \sqrt{6}}-\sqrt{7-2 \sqrt{6}}=$ _______________ .
View full solution →If $\sqrt{5+2 \sqrt{6}}=A+\sqrt{3}$, then $A=$ _______________ .
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 →Retionalise the denominator of each of the following: $\frac{3}{\sqrt5}$
View full solution →If $x=3+2 \sqrt{2}$, then find the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$.
View full solution →Simplify: $\sqrt{3-2 \sqrt{2}}$.
View full solution →Simplify: $\sqrt{3+2 \sqrt{2}}$.
View full solution →Write the rationalisation factor of $\sqrt{5}-2$.
View full solution →Simplify: $\sqrt{3+2\sqrt2}.$
View full solution →Write the rationalisation factor of $7-3\sqrt5.$
View full solution →Retionalise the denominator of each of the following: $\frac{\sqrt2+\sqrt5}{\sqrt3}$
View full solution →Find the value to three place of decimals of each of the following. It is given that $\sqrt2=1.414,\ \sqrt3=1.732,\ \sqrt5=2.236,\ \sqrt10=3.162.$ $\frac{\sqrt{2}-1}{\sqrt5}$
View full solution →Find the value to three place of decimals of each of the following. It is given that $\sqrt2=1.414,\ \sqrt3=1.732,\ \sqrt5=2.236,\ \sqrt10=3.162.$ $\frac{2+\sqrt{3}}{3}$
View full solution →If $\frac{\sqrt3-1}{\sqrt3+1}=\text{x}+\text{y}\sqrt3,$ find the value of $x$ and $y$.
View full solution →Rationales the denominator and simplify: $\frac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}$
View full solution →Find the value to three place of decimals of each of the following. It is given that $\sqrt2=1.414,\ \sqrt3=1.732,\ \sqrt5=2.236,\ \sqrt10=3.162.$
$\frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}$
View full solution →Express each one of the following with rational denominator: $\frac{\text{b}^2}{\sqrt{\text{a}^2+\text{b}^2}+\text{a}}$
View full solution →Express each one of the following with rational denominator: $\frac{6-4\sqrt2}{6+4\sqrt{2}}$
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 →If $\text{a}=\sqrt2+1,$ then write the value of $\text{a}-\frac{1}{\text{a}}.$
View full solution →Find the value of $\frac{6}{\sqrt5-\sqrt3},$ it being given that $\sqrt3=1.732$ and $\sqrt5=2.236.$
View full solution →Find the value of the following correct to three place of decimals, it begin that $\sqrt2=1.4142, \sqrt3=1.732,\ \sqrt5=2.2360,\ \sqrt6=2.4495$ and $\sqrt{10}=3.162.$ $\frac{3-\sqrt5}{3+2\sqrt5}$
View full solution →Simplify: $\frac{7+3\sqrt5}{3+\sqrt5}-\frac{7-3\sqrt5}{3-\sqrt5}$
View full solution →If $\text{x}=2+\sqrt3,$ find the value of $\text{x}^3+\frac{1}{\text{x}^3}.$
View full solution →