What is sqrt((4-9*8)^3) ?

The solution to sqrt((4-9*8)^3) is -136sqrt(17)i

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simplify sqrt((4-9*8)^3)

simplify

(4 - 9 \cdot 8)^{3}

- 13617 i

Solution steps

(4 - 9 \cdot 8)^{3}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((4 - 9 \cdot 8)^{3})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (4 - 9 \cdot 8)^{3 \cdot \frac{1}{2}}

3 \cdot \frac{1}{2} = \frac{3}{2}

= (4 - 9 \cdot 8)^{\frac{3}{2}}

Multiply the numbers:

9 \cdot 8 = 72

= (4 - 72)^{\frac{3}{2}}

Subtract the numbers:

4 - 72 = - 68

= (- 68)^{\frac{3}{2}}

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- 68)^{\frac{3}{2}} = (- 1)^{\frac{3}{2}} \cdot 6 8^{\frac{3}{2}}

= (- 1)^{\frac{3}{2}} \cdot 6 8^{\frac{3}{2}}

(- 1)^{\frac{3}{2}} = i^{3}

= i^{3} \cdot 6 8^{\frac{3}{2}}

6 8^{\frac{3}{2}} = (217)^{3}

= i^{3} (217)^{3}

Apply exponent rule:

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

(217)^{3} = 2^{3} (17)^{3}

= 2^{3} i^{3} (17)^{3}

(17)^{3} : 1 7^{\frac{3}{2}}

= i^{3} \cdot 2^{3} \cdot 1 7^{\frac{3}{2}}

1 7^{\frac{3}{2}} = 1717

= 2^{3} \cdot 1717 i^{3}

i^{3} = - i

= - 2^{3} \cdot 1717 i

2^{3} = 8

= - 8 \cdot 1717 i

Multiply the numbers:

8 \cdot 17 = 136

= - 13617 i

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