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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1. What is rationalisation and why is it important in mathematics? |
2. How do you rationalise the denominator of a fraction? |
3. Can you provide an example of rationalising the denominator? |
4. Are there any limitations or restrictions when rationalising the denominator? |
5. Can you rationalise the denominator if it contains a cube root or higher roots? |
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