What is sqrt((4tan^2(θ)+4)^3) ?

The solution to sqrt((4tan^2(θ)+4)^3) is 8(tan^2(θ)+1)^{3/2}

Popular >

simplify sqrt((4tan^2(θ)+4)^3)

simplify

(4 tan^{2} (θ) + 4)^{3}

8 (tan^{2} (θ) + 1)^{\frac{3}{2}}

Solution steps

(4 tan^{2} (θ) + 4)^{3}

Apply radical rule:

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

= ((4 tan^{2} (θ) + 4)^{3})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (4 tan^{2} (θ) + 4)^{3 \cdot \frac{1}{2}}

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

= (4 tan^{2} (θ) + 4)^{\frac{3}{2}}

Factor

4 tan^{2} (θ) + 4 : 4 (tan^{2} (θ) + 1)

= (4 (tan^{2} (θ) + 1))^{\frac{3}{2}}

Apply exponent rule:

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

= 4^{\frac{3}{2}} (tan^{2} (θ) + 1)^{\frac{3}{2}}

4^{\frac{3}{2}} = 8

= 8 (tan^{2} (θ) + 1)^{\frac{3}{2}}

(5 x^{\frac{7}{8}}) (7 x^{\frac{1}{4}})

\frac{1}{1.91 \cdot 1 0 ^{- 174}} (1.91 \cdot 1 0^{- 174})

(40 + 18) \cdot 1 0^{- 3} \cdot 9.8 \cdot (\frac{2}{2 \cdot 0.445 \cdot 175})^{2}

4^{1.5} \cdot 3 2^{- 0.6}

What is sqrt((4tan^2(θ)+4)^3) ?
The solution to sqrt((4tan^2(θ)+4)^3) is 8(tan^2(θ)+1)^{3/2}