shreyasingh85
Answered

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√(-√(3)+√(3+8√(7+4√(3))))

[tex]\sqrt{ - \sqrt{3} + \sqrt{3 + 8 \sqrt{7 + 4 \sqrt{3} } } } \\ [/tex]
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Sagot :

SalmonWorldTopper

Step-by-step explanation:

Given that: √[-√(3)+√{3+8√(7+4√(3))}]

= √[-√(3) + √{3+8√((√3)² + √(4)² + 2√(4*3))}]

= √[-√(3) + √{3 + 8√(√(3) + √(4))²}] [Since, {√(a) + √(b)}² = a+b + 2√(ab)]

= √[-√(3) + √{3 + 8√(√(3) + √(4))²}]

= √[-√(3) + √{3 + 8(√(3) + √(4))}]

= √[-√(3) + √{3 + 8(√(3) + √(2*2))}]

= √[-√(3) + √{3 + 8(√(3) + 2)}]

= √[-√(3) + √{3 + 16 + 8√(3)}]

= √[-√(3) + √{19 + 8√(3)}]

= √[-√(3) + √{16 + 3 + 2√(3*16)}]

= √[-√(3) + √{(16)² + (3)² + 2√(3*16)}]

= √[-√(3) + √{√(16)² + √(3)²}] [Since, {√(a) + √(b)}² = a+b + 2√(ab)]

= √{-√(3) + √(16) + √(3)}

= √{-√(3) + √(4*4) + √(3)}

= √{-√(3) + 4 + √(3)}

Now, cancel -√3 and +√3.

= √(4)

= √(2*2)

= 2

Answer: Hence, the simplified form of √[-√(3)+√{3+8√(7+4√(3))}] = 2.

Please let me know if you have any other questions.

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