What is sqrt(1+(2x-1/(8x))^2) ?

The solution to sqrt(1+(2x-1/(8x))^2) is (16x^2+1)/(8x)

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simplify sqrt(1+(2x-1/(8x))^2)

simplify

1 + (2 x - \frac{1}{8 x})^{2}

\frac{16 x ^{2} + 1}{8 x}

Solution steps

1 + (2 x - \frac{1}{8 x})^{2}

Simplify

1 + (2 x - \frac{1}{8 x})^{2} : \frac{256 x ^{4} + 32 x ^{2} + 1}{64 x ^{2}}

= \frac{256 x ^{4} + 32 x ^{2} + 1}{64 x ^{2}}

Apply radical rule:

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

assuming

a \geq 0, b \geq 0

= \frac{256 x ^{4} + 32 x ^{2} + 1}{64 x ^{2}}

Simplify

256 x^{4} + 32 x^{2} + 1 : 16 x^{2} + 1

= \frac{16 x ^{2} + 1}{64 x ^{2}}

Simplify

64 x^{2} : 8 x

= \frac{16 x ^{2} + 1}{8 x}

- \frac{1}{8} + \frac{1}{4}

(a + x)^{2}

\frac{f ( - 13 ) - ( - 13 - 12 h - 2 h ^{2} )}{h}

(h + 1)^{2}

x \cdot \frac{1}{2}

What is sqrt(1+(2x-1/(8x))^2) ?
The solution to sqrt(1+(2x-1/(8x))^2) is (16x^2+1)/(8x)