What is sqrt(x+\sqrt{x+1)}*sqrt(x+\sqrt{x-1)} ?

The solution to sqrt(x+\sqrt{x+1)}*sqrt(x+\sqrt{x-1)} is sqrt((x+\sqrt{x+1))(x+sqrt(x-1))}

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simplify sqrt(x+\sqrt{x+1)}*sqrt(x+\sqrt{x-1)}

simplify

x + x + 1 \cdot x + x - 1

(x + x + 1) (x + x - 1)

Solution steps

x + x + 1 x + x - 1

Apply radical rule:

a b = a \cdot b,

assuming

a \geq 0, b \geq 0

x + x + 1 x + x - 1 = (x + x + 1) (x + x - 1)

= (x + x + 1) (x + x - 1)

\frac{x ^{2} + 1}{x ^{2} - 1}

\frac{36}{- 49}

(b^{\frac{2}{3}} \cdot c^{\frac{2}{5}}) (b^{\frac{4}{9}} \cdot c^{\frac{9}{10}})

(x^{2} - 1)^{5}

(6 y^{\frac{1}{2}}) (9 y^{\frac{1}{2}})

What is sqrt(x+\sqrt{x+1)}*sqrt(x+\sqrt{x-1)} ?
The solution to sqrt(x+\sqrt{x+1)}*sqrt(x+\sqrt{x-1)} is sqrt((x+\sqrt{x+1))(x+sqrt(x-1))}