Question

√(28-10√(3))-√7+4√(3))​

Answer 1

Answer:

√(28-10√(3))-√7+4√(3))​ = 6.5

Step-by-step explanation:

From the above question,

√(28-10√(3))-√7+4√(3))​

(28 - 10*3^1/2) ^1/2 - (7 +4*3^1/2) ^-1/2

       = (28 - 2*75^1/2) ^1/2 - (7 +2*12^1/2) ^-1/2

       = (25 + 3 - 2*5*3^1/2) ^1/2 - (4 + 3 +2*2*3^1/2) ^-1/2

       = (5^2 + (sqrt(3))^2 - 2*5*3^1/2) ^1/2 - (2^2 + (sqrt(3))^2 +2*3^1/2) ^-1/2

       = (5 - sqrt(3)) - (2+sqrt(3))^-1

       = (5 - sqrt(3)) - (2 - sqrt(3))

       = 3

√[(5 + √3)]2 – √[(2 - √3)]2

       = 5 + √3 – (2 - √3)

       = 5 + √3 – 2 + √3  

       = 3 + 2√3

       = 3 + 2 × 1.72

       = 3 + 3.44

       = 6.44

       = 6.5

For more related question : https://brainly.in/question/7425439

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