Answer :

GinnyAnswer
To simplify the expression
[tex]\[ -3 i \sqrt{-40} \][/tex]

we can follow these steps:

1. Simplify the square root of [tex]\(-40\)[/tex]:

We know that the square root of a negative number can be expressed in terms of the imaginary unit [tex]\( i \)[/tex]. Recall that:
[tex]\[ \sqrt{-1} = i \][/tex]

Therefore:
[tex]\[ \sqrt{-40} = \sqrt{40} \cdot \sqrt{-1} = \sqrt{40} \cdot i \][/tex]

2. Simplify [tex]\(\sqrt{40}\)[/tex]:

[tex]\[ \sqrt{40} \approx 6.324555320336759 \][/tex]

Hence:
[tex]\[ \sqrt{-40} = 6.324555320336759 \cdot i \][/tex]

3. Insert this back into the original expression:
[tex]\[ -3 i \sqrt{-40} = -3 i \cdot (6.324555320336759 \cdot i) \][/tex]

4. Multiply the terms:

Recall that [tex]\( i^2 = -1 \)[/tex], so:
[tex]\[ -3 i \cdot 6.324555320336759 \cdot i = -3 \cdot 6.324555320336759 \cdot i^2 \][/tex]

5. Simplify using [tex]\( i^2 = -1 \)[/tex]:
[tex]\[ -3 \cdot 6.324555320336759 \cdot (-1) = 3 \cdot 6.324555320336759 \][/tex]

6. Calculate the final result:
[tex]\[ 3 \cdot 6.324555320336759 = 18.973665961010275 \approx 18.97 \][/tex]

The simplified form of the expression [tex]\(-3 i \sqrt{-40}\)[/tex] is:
[tex]\[ 18.97 \][/tex]

Other Questions