What is 3sqrt(-125) ?

The solution to 3sqrt(-125) is 15sqrt(5)i

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simplify 3sqrt(-125)

simplify

3 - 125

155 i

Solution steps

3 - 125

Prime factorization of

125 : 5^{3}

= 3 - 5^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

- 5^{3} = - 5^{2} \cdot 5

= 3 - 5^{2} \cdot 5

Apply radical rule:

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

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

= 3 5^{2} - 5

Apply radical rule:

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

5^{2} = 5

= 3 \cdot 5 - 5

Multiply the numbers:

3 \cdot 5 = 15

= 15 - 5

Apply radical rule:

- a = a - 1

- 5 = 5 - 1

= 155 - 1

Apply imaginary number rule:

- 1 = i

= 155 i

7 < x < 9

(s^{4} t)^{2} (s t)

33 \cdot 421

60 2^{2} + 72 4^{2} = c^{2}