What is (a^4+a^{-4}+2)^{1/2} ?

The solution to (a^4+a^{-4}+2)^{1/2} is ((a^2+2^{1/2}a+1)(a^2-2^{1/2}a+1))/(a^2)

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simplify (a^4+a^{-4}+2)^{1/2}

simplify

(a^{4} + a^{- 4} + 2)^{\frac{1}{2}}

\frac{( a ^{2} + 2 ^{\frac{1}{2}} a + 1 ) ( a ^{2} - 2 ^{\frac{1}{2}} a + 1 )}{a ^{2}}

Solution steps

(a^{4} + a^{- 4} + 2)^{\frac{1}{2}}

Simplify

a^{4} + a^{- 4} + 2 : \frac{a ^{8} + 1 + 2 a ^{4}}{a ^{4}}

= (\frac{a ^{8} + 1 + 2 a ^{4}}{a ^{4}})^{\frac{1}{2}}

Apply exponent rule:

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

= \frac{( a ^{8} + 1 + 2 a ^{4} ) ^{\frac{1}{2}}}{( a ^{4} ) ^{\frac{1}{2}}}

Simplify

(a^{4})^{\frac{1}{2}} : a^{2}

= \frac{( a ^{8} + 1 + 2 a ^{4} ) ^{\frac{1}{2}}}{a ^{2}}

(a^{8} + 1 + 2 a^{4})^{\frac{1}{2}} = (a^{2} + 2^{\frac{1}{2}} a + 1) (a^{2} - 2^{\frac{1}{2}} a + 1)

= \frac{( a ^{2} + 2 ^{\frac{1}{2}} a + 1 ) ( a ^{2} - 2 ^{\frac{1}{2}} a + 1 )}{a ^{2}}

(- 1.4) y (4.6)

((5 \cdot 2)^{1 0^{20}})^{5}

\frac{1}{cos ^{2} ( t ) - 1}

x - 0.25 x

\frac{36 z ^{7} - 24 z ^{3}}{4 z ^{3}}

What is (a^4+a^{-4}+2)^{1/2} ?
The solution to (a^4+a^{-4}+2)^{1/2} is ((a^2+2^{1/2}a+1)(a^2-2^{1/2}a+1))/(a^2)