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# Simplify each of the following expressions:

(i) (3 + √3)(2 + √2) (ii) (3 + √3)(3 - √3) (iii) (√5 + √2)² (iv) (√5 - √2)(√5 + √2)

**Solution:**

(i) (3 + √3)(2 + √2)

By Distributive property, (a + b) (c + d) = ac + ad + bc + bd

(3 + √3)(2 + √2) = 3 × 2 + 3√2 + √3 × 2 + √3 × √2

= 6 + 3√2 + 2√3 + √6

(ii) (3 + √3)(3 - √3)

Using the identity, (a + b) (a - b) = a² - b²

(3 + √3)(3 - √3) = 3² - (√3)²

= 9 - 3

= 6

(iii) (√5 + √2)²

Using the identity, (a + b) ² = a² + 2ab + b²

(√5 + √2)² = (√5)² + (2×√5×√2) + (√2)²

= (5 + 2√10 + 2)

= 7 + 2√10

(iv) (√5 - √2)( √5 + √2)

Using the identity (a + b) (a - b) = a² - b²

(√5 - √2)( √5 + √2) = (√5)² - (√2)²

= 5 - 2

= 3

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 1 Number Systems

**Video Solution:**

## Simplify each of the following expressions: (i) (3 + √3)(2 + √2) (ii) (3 + √3)(3 - √3) (iii) (√5 + √2)² (iv) (√5 - √2)(√5 + √2)

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.5 Question 2:

**Summary:**

Thus, the simplified values of (3 + √3) (2 + √2), (3 + √3) (3 - √3), (√5 + √2)², and (√5 - √2) (√5 + √2) are 6 + 3√2 + 2√3 + √6, 6, 7 + 2√10 and 3 respectively.

**☛ Related Questions:**

- Recall, π is defined as the ratio of circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
- Represent √9.3 on the number line.
- Rationalize the denominators of the following: i) 1/√7 ii) 1/(√7 - √6) iii) 1/(√5 + √2) iv) 1/(√7 - 2)
- Classify the following numbers as rational or irrational: i) 2 - √5 ii) (3 + √23) - √23 iii) 2√7 ÷ 2√7 iv) 1/√2 v) 2π.

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