What is (2+x^2)^{1/2}(1+(2+x^2)^{1/2})^{1/2} ?

The solution to (2+x^2)^{1/2}(1+(2+x^2)^{1/2})^{1/2} is ((x^2+2)((x^2+2)^{1/2}+1))^{1/2}

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simplify (2+x^2)^{1/2}(1+(2+x^2)^{1/2})^{1/2}

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

(x^{2} + 2)^{\frac{1}{2}} ((x^{2} + 2)^{\frac{1}{2}} + 1)^{\frac{1}{2}} = ((x^{2} + 2) ((x^{2} + 2)^{\frac{1}{2}} + 1))^{\frac{1}{2}}

= ((x^{2} + 2) ((x^{2} + 2)^{\frac{1}{2}} + 1))^{\frac{1}{2}}

\frac{x + 9}{x + 8}

1.2 \cdot e^{- 0.89 s^{- 1} 6}

3^{\frac{2}{5}} b^{\frac{2}{5}}

1.4 \cdot 1 0^{- 14}

- (2.33 \cdot 1 0^{- 8}) \frac{- 4 - 4}{5.33 \cdot 1 0 ^{- 3}}

What is (2+x^2)^{1/2}(1+(2+x^2)^{1/2})^{1/2} ?
The solution to (2+x^2)^{1/2}(1+(2+x^2)^{1/2})^{1/2} is ((x^2+2)((x^2+2)^{1/2}+1))^{1/2}