Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma Solutions: Rationalisation- 1
Rationalisation- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download
RD Sharma Solutions: Exercise 3.1 - Rationalisation
Q.1. Simplify each of the following:
(i)
(ii)
Proof: (i) We know that
. We will use this property to simplify the expression
.
Hence the value of the given expression is 4.
(ii) We know that
. We will use this property to simplify the expression
.
Hence the value of the given expression is 5.
Q.2. Simplify the following expressions:
(i) (4+√7) (3+√2)
(ii) (3+√3) (5−√2)
(iii) (√5−2) (√3−√5)
Proof: (i) We can simplify the expression (4+√7) (3+√2) as
Hence the value of the expression is
.
(ii) We can simplify the expression (3+√3) (5−√2) as
Hence the value of the expression is
.
(iii) We can simplify the expression (√5−2) (√3−√5) as
Hence the value of the expression is
.
Q.3. Simplify the following expressions:
(i) (11+√11) (11−√11)
(ii) (5+√7) (5−√7)
(iii) (√8−√2) (√8+√2)
(iv) (3+√3)(3−√3)
(v) (√5−√2) (√5+√2)
Proof: (i) We know that
. We will use this property to simplify the expression (11+√11) (11−√11)
= 110
Hence the value of expression is 110.
(ii) We know that
. We will use this property to simplify the expression (5+√7) (5−√7) .
= 18
Hence the value of expression is 18.
(iii) We know that
. We will use this property to simplify the expression
.
= 6
Hence the value of expression is 6
(iv) We know that
. We will use this property to simplify the expression
.
= 6
Hence the value of expression is 6.
(v) We know that
. We will use this property to simplify the expression
.
= 3
Hence the value of expression is 3.
Q.4. Simplify the following expressions:
(i) (√3+√7)2
(ii) (√5−√3)2
(iii) (2√5+3√2)2
Proof: (i) We know that
. We will use this property to simplify the expression
.
Hence the value of expression is
(ii) We know that
. We will use this property to simplify the expression
.
Hence the value of expression is
(iii) We know that
. We will use this property to simplify the expression
.
Hence the value of expression is
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FAQs on Rationalisation- 1 RD Sharma Solutions - Mathematics (Maths) Class 9
| 1. What is rationalisation and why is it important in mathematics? |  |
Ans. Rationalisation is the process of eliminating radicals or irrational numbers from the denominator of a fraction. It is important in mathematics because it helps simplify the expressions, makes them easier to work with, and often provides a more accurate representation of the numbers involved.
| 2. How do you rationalise the denominator of a fraction? | |
Ans. To rationalise the denominator of a fraction, you multiply both the numerator and denominator by a suitable expression such that the denominator no longer contains square roots or other radicals. This is done to eliminate any irrational numbers from the denominator and simplify the fraction.
| 3. Can you provide an example of rationalising the denominator? | |
Ans. Certainly! Let's consider the fraction 1 / (√2 + √3). To rationalise the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is (√2 - √3). After simplifying, we get (√2 - √3) / (2 - √6).
| 4. Are there any limitations or restrictions when rationalising the denominator? | |
Ans. Yes, there are certain limitations or restrictions when rationalising the denominator. One restriction is that the expression inside the radical should not have any perfect square factors in the denominator. If it does, then the rationalisation process may not be applicable or may need to be modified.
| 5. Can you rationalise the denominator if it contains a cube root or higher roots? | |
Ans. No, the process of rationalising the denominator is specifically for eliminating square roots or radicals with index 2. It does not apply to cube roots or higher roots. For expressions containing cube roots or higher roots, a different approach or method needs to be used to simplify the expression.
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