What is sqrt(x)sqrt(1+1/(4x)) ?

The solution to sqrt(x)sqrt(1+1/(4x)) is (sqrt(4x+1))/2

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simplify sqrt(x)sqrt(1+1/(4x))

simplify

x 1 + \frac{1}{4 x}

\frac{4 x + 1}{2}

Solution steps

x 1 + \frac{1}{4 x}

Simplify

1 + \frac{1}{4 x} : \frac{4 x + 1}{2 x}

= x \frac{4 x + 1}{2 x}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x 4 x + 1}{2 x}

Cancel the common factor:

x

= \frac{4 x + 1}{2}

\frac{- x ^{2} + 3 x - 7 + h - ( - x ) 2 + 3 x - 7}{h}

- 6^{6}

\frac{- 6}{8 + 2}

- 9 a^{2}

What is sqrt(x)sqrt(1+1/(4x)) ?
The solution to sqrt(x)sqrt(1+1/(4x)) is (sqrt(4x+1))/2