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AP DSC School Assistant Math Model Test 2

Section: Subject Specific

Question : 107 of 160

Marks: +1, -0

The value of

(\sqrt{-6}\times \sqrt{-6})

is:

Solution:

Concept:

The square root of a negative number involves the imaginary unit

i = \sqrt{-1}

, where

i^2 = -1

. The product of two square roots simplifies by first expressing each as a real part times

i

Explanation:

We are asked to find

(\sqrt{-6} \times \sqrt{-6})

Step 1: Write each square root using

i

\sqrt{-6} = \sqrt{6} \cdot i

Step 2: Multiply:

(\sqrt{6} \cdot i) \times (\sqrt{6} \cdot i) = (\sqrt{6} \times \sqrt{6}) \times (i \times i) = 6 \times i^2

Step 3: Since

i^2 = -1

, we have

6 \times (-1) = -6

Thus the product is

-6

Answer:

Option B:

-6

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