Question

under root minus 3 under root minus 6 is equal to​

Answer 1

$\sf \sqrt{ - 3} \times \sqrt{ - 6} = - 3 \sqrt{2}$

Given :

The expression

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

To find :

To simplify the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

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

Step 2 of 2 :

Simplify the expression

We know that i is the complex number satisfying the property that i² = - 1

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

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

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

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

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

$\sf = ( - 1) \times \sqrt{ 3 \times 3 \times 2}$

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

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