Rationalise 41+2+3
Explanation:
Given, 41+2+3
We first multiply and divide by 1 - (√2 + √3)
∴41+2+3 = 41+2+3 × 1-(2+3)1-(2+3)
⇒ 41+2+3 = 41-(2+3)12-(2+3)2
⇒ 41+2+3 = 41-(2+3)1-(5+26)
⇒ 41+2+3 = 41-(2+3)-(4+26)
⇒ 41+2+3 = 2(2+3)-12+6
Now, we multiply and divide by 2 - √6
⇒ 41+2+3 = 2(2+3)-12+6 × 2-62-6
⇒ 41+2+3 = 2(2+3)-1×(2-6)22-62
⇒ 41+2+3 = 2(2+3)-1×(2-6)-2
⇒ 41+2+3 = [(√2 + √3) - 1] × (√6 - 2)
⇒ 41+2+3 = √12 - 2√2 + √18 - 2√3 - √6 + 2
⇒ 41+2+3 = 2√3 - 2√2 + 3√2 - 2√3 - √6 + 2
⇒ 41+2+3 = √2 - √6 + 2
Hence, option (c).
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