Question

rationalise the denominator of 1/4+root2+root5

Answer 1

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Answer 2

Answer:

(36 - 19 √2 - 13 √5 + 8 √10 ) / 167.

Step-by-step explanation:

Rationalizing the denominator:

1 / ( 4 + √2 + √5 )

Multiply and divide the expression by ( 4 + √2 - √5 )

= 1 / ( 4 + √2 + √5 )   ×   ( 4 + √2 - √5 ) / ( 4 + √2 - √5 )

= ( 4 + √2 - √5 ) / [( 4 + √2)² - ( √5 )²]

= ( 4 + √2 - √5 ) / [16 + 2 + 8 √2 - 5]

= ( 4 + √2 - √5 ) / [13 + 8 √2 ]

Multiply and divide the expression by [13 - 8 √2 ]:

= ( 4 + √2 - √5 ) / [13 + 8 √2 ]   ×   [13 - 8 √2 ] / [13 - 8 √2 ]

= (52 - 32 √2 + 13 √2 - 16 - 13 √5 + 8 √10) / (169 - 2)

= 36 - 19 √2 - 13 √5 + 8 √10  / 167.

Therefore, after rationalizing the denominator, we get (36 - 19 √2 - 13 √5 + 8 √10 ) / 167.

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