What is (sqrt(-75))^2 ?

The solution to (sqrt(-75))^2 is -75

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simplify (sqrt(-75))^2

simplify

(- 75)^{2}

- 75

Solution steps

(- 75)^{2}

- 75 = 3 \cdot 5 i

= (3 \cdot 5 i)^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 \cdot 5 i)^{2} = (3)^{2} \cdot 5^{2} i^{2}

= (3)^{2} \cdot 5^{2} i^{2}

5^{2} = 25

= (3)^{2} \cdot 25 i^{2}

(3)^{2} = 3

= 3 \cdot 25 i^{2}

Multiply the numbers:

3 \cdot 25 = 75

= 75 i^{2}

Apply imaginary number rule:

i^{2} = - 1

= 75 (- 1)

Multiply the numbers:

75 (- 1) = - 75

= - 75

(6.67 \cdot 1 0^{- 11}) (5.97 \cdot 1 0^{24})

e^{- a t} sin (wt)

(4 x) (3 x^{2})

1 0^{- 6}