(B) To find the rationalising factor of an expression of the form $a - \sqrt{b}$,we multiply it by its conjugate $a + \sqrt{b}$ to eliminate the squar

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) To find the rationalising factor of an expression of the form $a - \sqrt{b}$,we multiply it by its conjugate $a + \sqrt{b}$ to eliminate the square root.Here,the given expression is $4 - \sqrt{5}$.Multiplying $4 - \sqrt{5}$ by $4 + \sqrt{5}$ gives $(4)^2 - (\sqrt{5})^2 = 16 - 5 = 11$,which is a rational number.Therefore,the rationalising factor of $4 - \sqrt{5}$ is $4 + \sqrt{5}$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Easy

For each question,select the proper option from four options given,to make the statement true: The rationalising factor of $4-\sqrt{5}$ is...........

A
$4-\sqrt{5}$
B
$4+\sqrt{5}$
C
$\sqrt{5}-4$
D
$5-\sqrt{4}$

Explore More

Browse All

Question Bank

All Subjects

Class 9 Questions

Class 9

Mathematics Questions

Chapter

Number Systems

Subtopic

Mix Examples - Number Systems

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$

Medium

View Solution

If $125^{x} = \frac{25}{5^{x}},$ then find the value of $x$.

Medium

View Solution

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.
$\frac{6}{\sqrt{6}}$

Difficult

View Solution

The number obtained on rationalizing the denominator of $\frac{1}{7-\sqrt{2}}$ is

Easy

View Solution

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

For each question,select the proper option from four options given,to make the statement true: The rationalising factor of $4-\sqrt{5}$ is...........

Similar Questions

Convert the following rational number into decimal form and state the kind of its decimal expansion:$\frac{29}{12}$

If $125^{x} = \frac{25}{5^{x}},$ then find the value of $x$.

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.$\frac{6}{\sqrt{6}}$

The number obtained on rationalizing the denominator of $\frac{1}{7-\sqrt{2}}$ is

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.
$\frac{6}{\sqrt{6}}$