plz answer this question's
Answers
Answer:
HOPE ITS HELP YOU
HOPE ITS HELP YOU
Question:
1. Classify the given numbers as rational or irrational:
2. Simplify the given expressions:
Answer:
1.
Rational numbers:
( ii ) ( 3 + √23 ) - √23
( iii ) ( 2 √7 ) / ( 7 √7 )
Irrational numbers:
( i ) 2 - √5
( iv ) 1 / √2
( v ) 2 π
─────────────────────
2.
( i ) ( 3 + √3 ) ( 2 + √2 ) = 6 + 3 √2 + 2 √3 + √6
( ii ) ( 3 + √3 ) ( 3 - √3 ) = 6
( iii ) ( √5 + √2 )² = 7 + 2 √10
( iv ) ( √5 - √2 ) ( √5 + √2 ) = 3
Step-by-step-explanation:
1.
( i ) 2 - √5
Here, 2 is a rational number and √5 is an irrational number.
We know that, addition or subtraction of any rational and irrational number is always an irrational number.
∴ 2 - √5 is an irrational number.
( ii ) ( 3 + √23 ) - √23
⇒ 3 + √23 - √23
⇒ 3 + 0
⇒ 0
0 is a rational number.
∴ ( 3 + √23 ) - √23 is a rational number.
( iii ) ( 2 √7 ) / ( 7 √7 )
⇒ 2 ÷ 7 * √7 ÷ √7
⇒ 2 ÷ 7 * 1
⇒ 2 ÷ 7
⇒ 2 / 7
2 / 7 is a rational number.
∴ ( 2 √7 ) / ( 7 √7 ) is a rational number.
( iv ) 1 / √2
Here, 1 is rational number and √2 is an irrational number.
We know that, division of a rational and an irrational number is always an irrational number.
∴ 1 / √2 is an irrational number.
( v ) 2 π
Here, 2 is a rational number and π is an irrational number.
We know that, product of a rational and irrational number is always an irrational number.
∴ 2 π is an irrational number.
─────────────────────
2.
( i ) ( 3 + √3 ) ( 2 + √2 )
⇒ ( 3 * 2 + 3 * √2 ) + ( √3 * 2 + √3 * √2 )
⇒ ( 6 + 3 √2 ) + ( 2 √3 + √6 )
⇒ 6 + 3 √2 + 2 √3 + √6
( ii ) ( 3 + √3 ) ( 3 - √3 )
⇒ ( 3 )² - ( √3 )² - - [ ( a + b ) ( a - b ) = a² - b² ]
⇒ 3 * 3 - √3 * √3
⇒ 9 - √9
⇒ 9 - 3
⇒ 6
( iii ) ( √5 + √2 )²
⇒ ( √5 )² + 2 * √5 * √2 + ( √2 )² - - [ ( a + b )² = a² + 2ab + b² ]
⇒ 5 + 2 * √10 + 2
⇒ 5 + 2 √10 + 2
⇒ 5 + 2 + 2 √10
⇒ 7 + 2 √10
( iv ) ( √5 - √2 ) ( √5 + √2 )
⇒ ( √5 )² - ( √2 )² - - [ ( a + b ) ( a - b ) = a² - b² ]
⇒ √5 * √5 - √2 * √2
⇒ √25 - √4
⇒ 5 - 2
⇒ 3