Question

$( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }$
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Answer 1

ANSWER:

$( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} } = 2$

GIVEN:

$( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }$

TO FIND:

The value of $( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }$

EXPLANATION:

$( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }$

$= \sqrt[3]{ (\sqrt{11} + \sqrt{3})( \sqrt{11} - \sqrt{3} ) }$

(A + B)(A - B) = (A² - B²)

$= \sqrt[3]{ (\sqrt{11})^{2} - (\sqrt{3})^{2} }$

$= \sqrt[3]{ 11 - 3 }$

$= \sqrt[3]{ 8 }$

$= 2$

$( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} } = 2$

SOME OTHER FORMULAE:

• (A + B)² = A² + 2AB + B²

• (A - B)² = A² - 2AB + B²

• A² + B² = (A + B)² - 2AB

• A² + B² = (A - B)² + 2AB

• A³ - B³ = (A - B)(A² + AB + B²)

• A³ + B³ = (A + B)(A² - AB + B²)

• A³ + B³ + C³ = 3ABC ( A + B + C = 0)

• (A - B)³ = A³ - B³ - 3AB(A - B)

• (A + B)³ = A³ + B³ + 3AB(A + B)