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Popular >

simplify (sqrt(-75))^3

Solution

simplify

(- 75)^{3}

Solution

- 3753 i

Solution steps

(- 75)^{3}

- 75 = 3 \cdot 5 i

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

Apply exponent rule:

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

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

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

5^{3} = 125

= (3)^{3} \cdot 125 i^{3}

(3)^{3} = 33

= 3 \cdot 1253 i^{3}

Multiply the numbers:

3 \cdot 125 = 375

= 3753 i^{3}

Simplify

i^{3} : - i

= 3753 (- i)

Apply rule:

a (- b) = - ab

3753 (- i) = - 3753 i

= - 3753 i

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Frequently Asked Questions (FAQ)

What is (sqrt(-75))^3 ?
The solution to (sqrt(-75))^3 is -375sqrt(3)i