What is sqrt(1+(x^3-1/(4x^3))^2) ?

The solution to sqrt(1+(x^3-1/(4x^3))^2) is (sqrt(16x^{12)+8x^6+1})/(4x^3)

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simplify sqrt(1+(x^3-1/(4x^3))^2)

simplify

1 + (x^{3} - \frac{1}{4 x ^{3}})^{2}

\frac{16 x ^{12} + 8 x ^{6} + 1}{4 x ^{3}}

Solution steps

1 + (x^{3} - \frac{1}{4 x ^{3}})^{2}

Simplify

1 + (x^{3} - \frac{1}{4 x ^{3}})^{2} : \frac{16 x ^{12} + 8 x ^{6} + 1}{16 x ^{6}}

= \frac{16 x ^{12} + 8 x ^{6} + 1}{16 x ^{6}}

Apply radical rule:

\frac{a}{b} = \frac{a}{b},

assuming

a \geq 0, b \geq 0

= \frac{16 x ^{12} + 8 x ^{6} + 1}{16 x ^{6}}

Simplify

16 x^{6} : 4 x^{3}

= \frac{16 x ^{12} + 8 x ^{6} + 1}{4 x ^{3}}

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lo g_{4} (28)

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What is sqrt(1+(x^3-1/(4x^3))^2) ?
The solution to sqrt(1+(x^3-1/(4x^3))^2) is (sqrt(16x^{12)+8x^6+1})/(4x^3)