find the square root of (2-root5) in the form of root a - root b
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find the square root of (2-root5) in the form of root a - root b
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Given : 2 - √5
To find : square root in the form of root a - root b
Solution:
Let say
√a - √b is the Square root of 2 - √5
=> (√a - √b )² = 2 - √5
=> a + b - 2√ab = 2 - √5
=> a + b = 2
2√ab = √5
=> 4ab = 5
=> ab = 5/4
Hence a & b are roots of Equation
x² - 2x + 5/4 = 0
=> x = (2 ± √(4 - 5) )/2
=> x = ( 2 ± i)/2
a = ( 2 + i)/2 , b = ( 2 - i)/2
Square root of 2 - √5 = √ (( 2 + i)/2 ) - √ (( 2 - i)/2 )
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