Question

Two classmates Salma and Anil simplified two different expressions during the revision hour and explained to each other their simplifications. Salma explains simplification of √ 2/√5 +√3 by rationalizing the denominator and Anil explains
simplifications of (√2 + √3)(√2 − √3) by using the identity (a + b)(a − b). Answer the following question.
1. What is the conjugate of √5 + √3.
a) √5 + √3
b) √5 − √3
c) √5 × √3
d) √5/√3

2. By rationalizing the denominator of √ 2/√5 +√3
Salma got the answer:
a) √ 2/√5 −√3
b) √ 2(√5 −√3)/2
c) √5 − √3
d) √ 2(√5 +√3)/2

3. Anil applied _______ identity to solve (√5 + √7)(√5 − √7)
a) (a + b) (a + b)
b) (a + b) (a − b)
c) (a − b) (a − b)
d) a^2+2ab+b^2


4. (√2 + √3)(√2 − √3) =________
a) −1
b) 1
c) 5
d) -5

5.Addition of two irrational numbers is equal to _______.
a) Rational
b) Irrational
c) Integers
d) Whole Number

Answer 1

Question (1) :- 1. What is the conjugate of √5 + √3.

a) √5 + √3

b) √5 − √3

c) √5 × √3

d) √5/√3

Answer :-

we know that, to find the conjugate of binomial surds, we changes the sign in between the terms, that is,

• '+' becomes '-' .
• '-' becomes '+'.

therefore, the conjugate of √5 + √3 is √5 - √3 . (Option b) .

Question (2) :- By rationalizing the denominator of √ 2/√5 +√3

Salma got the answer:

a) √ 2/√5 −√3

b) √ 2(√5 −√3)/2

c) √5 − √3

d) √ 2(√5 +√3)/2

Solution :-

→ √2/(√5 + √3)

rationalizing the denominator we get,

→ {√2/(√5 + √3)} * {(√5 - √3)/(√5 - √3)}

→ {√2 * (√5 - √3)} / {(√5 + √3) * (√5 - √3)}

using (a + b)(a - b) = a² - b² in denominator now,

→ {√2 * (√5 - √3)} /{(√5)² - (√3)²}

→ {√2 * (√5 - √3)} / (5 - 3)

→ {√2 * (√5 - √3)} / 2

→ √2(√5 - √3)/2 (Option b)

Question (3) :- Anil applied _______ identity to solve (√5 + √7)(√5 − √7)

a) (a + b) (a + b)

b) (a + b) (a − b)

c) (a − b) (a − b)

d) a^2+2ab+b^2

Solution :-

→ (√5 + √7)(√5 − √7)

Let ,

• √5 = a
• √7 = b

then,

→ (√5 + √7)(√5 − √7) = (a + b)(a - b) (Option b) .

Question (4) :- (√2 + √3)(√2 − √3) =________

a) −1

b) 1

c) 5

d) -5

Solution :-

using (a + b)(a - b) = a² - b² we get,

→ (√2)² - (√3)²

→ 2 - 3

→ (-1) (Option a) .

Question (5) :- Addition of two irrational numbers is equal to _______.

a) Rational

b) Irrational

c) Integers

d) Whole Number

Solution :-

Addition of two irrational numbers is equal to Irrational number . (Option b).

Note :- if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Answer 2

Answer:

1. (b) √5-√4

2. (c) √5-√3

3. (b) (a+b) (a-b)

4. (a) -1

5. Rational