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Popular >

simplify sqrt((-5y)^3)

Solution

simplify

(- 5 y)^{3}

Solution

- 55 i y^{\frac{3}{2}}

Solution steps

(- 5 y)^{3}

Apply radical rule:

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

= ((- 5 y)^{3})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (- 5 y)^{3 \cdot \frac{1}{2}}

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

= (- 5 y)^{\frac{3}{2}}

Apply exponent rule:

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

(- 5 y)^{\frac{3}{2}} = (- 1)^{\frac{3}{2}} (5 y)^{\frac{3}{2}}

= (- 1)^{\frac{3}{2}} (5 y)^{\frac{3}{2}}

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

= i^{3} (5 y)^{\frac{3}{2}}

Apply exponent rule:

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

(5 y)^{\frac{3}{2}} = 5^{\frac{3}{2}} y^{\frac{3}{2}}

= 5^{\frac{3}{2}} i^{3} y^{\frac{3}{2}}

5^{\frac{3}{2}} = 55

= 55 i^{3} y^{\frac{3}{2}}

i^{3} = - i

= - 55 i y^{\frac{3}{2}}

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Frequently Asked Questions (FAQ)

What is sqrt((-5y)^3) ?
The solution to sqrt((-5y)^3) is -5sqrt(5)iy^{3/2}