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If \( \Large \sqrt{28 - 6\sqrt{3}} = \sqrt{3} a + b \), (where a, b are rationale), value of \( \Large \left(a + b\right) \) is

A) -2
B) 2
C) 1
D) -1

Correct Answer:

A) -2

Description for Correct answer:

\( \Large \sqrt{28-6\sqrt{3}} = \sqrt{3} a + b \)

=> \( \Large \sqrt{ \left(1\right)^{2} + \left(3\sqrt{3}\right)^{2} - 6\sqrt{3} } = \sqrt{3}a + b \)

=> \( \Large \sqrt{ \left(1 - 3\sqrt{3}\right)^{2} } = \sqrt{3}a + b \)

=> \( \Large \left(1 - 3\sqrt{3}\right) = \sqrt{3}a + b \)

On comparing, we get

\( \Large a = -3, b =1 \)

Therefore, a + b = -3 + 1 = 2

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

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