What is 5sqrt(-100) ?

The solution to 5sqrt(-100) is 50i

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simplify 5sqrt(-100)

simplify

5 - 100

50 i

Solution steps

5 - 100

Prime factorization of

100 : 2^{2} \cdot 5^{2}

= 5 - 2^{2} \cdot 5^{2}

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

- 2^{2} \cdot 5^{2} = 2^{2} - 5^{2}

= 5 2^{2} - 5^{2}

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 5 \cdot 2 - 5^{2}

5^{2} = 25

= 5 \cdot 2 - 25

Multiply the numbers:

5 \cdot 2 = 10

= 10 - 25

Apply radical rule:

- a = a - 1

- 25 = 25 - 1

= 1025 - 1

Apply imaginary number rule:

- 1 = i

= 1025 i

25 = 5

= 10 \cdot 5 i

Multiply the numbers:

10 \cdot 5 = 50

= 50 i

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