Question

root-3 root-6 is equal to

Answer 1

Given : root-3 root-6

√-3 x √-6

To Find :   Simplify

Solution:

√-3 x √-6

√-3  = √(3)*(-1) = √3 x √(-1)  = i√3

√-6 = √(6)*(-1) = √6 x √(-1)  = i√6

√-3 x √-6

=  i√3 x  i√6

= i² x √3x6

= i² x √3x3x2

=  i² x 3√2

i² = - 1

= - 3√2

√-3 x √-6  = - 3√2

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Answer 2

SOLUTION

TO DETERMINE

$\sf{ \sqrt{ - 3} \times \sqrt{ - 6} }$

EVALUATION

FIRST METHOD

$\sf{ \sqrt{ - 3} \times \sqrt{ - 6} }$

$\sf{ = \sqrt{ 3 \times ( - 1)} \times \sqrt{ 6 \times ( - 1)} }$

$\sf{ = \sqrt{ 3} \times \sqrt{ - 1} \times \sqrt{ 6} \times \sqrt{ - 1} }$

$\sf{ = \sqrt{ 3} \times i \times \sqrt{ 6} \times i}$

$\sf{ = \sqrt{ 3 \times 6} \times {i}^{2} }$

$\sf{ = - \sqrt{ 3 \times 6} }$

$\sf{ = - \sqrt{ 3 \times 3 \times 2} }$

$\sf{ = -3 \sqrt{ 2} }$

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