Math, asked by gcveerabhadrappagvva, 5 months ago

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Answered by rosemary139
2

Answer:

HOPE ITS HELP YOU

HOPE ITS HELP YOU

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Answered by varadad25
10

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

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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.

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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

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