Question

Select True or False for each statement.

Answer 1

$\left( \dfrac 1 {64} \right)^{- 5/6} =64^{5/6} = (\sqrt[6]{64})^5 = 2^5 =32$

TRUE

$\sqrt[5]{36^4}=36^{4/5}$

which surely isn't 36.  FALSE

$\sqrt{12} - \dfrac 2 5 \sqrt{75} = 2 \sqrt{3} -\dfrac 2 5 (5) \sqrt{3} = 0$

FALSE

For the fourth one we have a

$\sqrt{98b} + \sqrt{2b}$

which isnt

$10\sqrt{b}$

so this is FALSE.

$\dfrac{1}{(\sqrt 5 - \sqrt 6)^2}$

$= \dfrac{1}{(\sqrt 5 - \sqrt 6)^2} \cdot \dfrac{(\sqrt 5 + \sqrt 6)^2}{(\sqrt 5 + \sqrt 6)^2}$

$= \dfrac{(\sqrt 5 + \sqrt 6)^2}{ ( (\sqrt 5 - \sqrt 6)(\sqrt 5 + \sqrt 6))^2}$

$= \dfrac{(\sqrt 5 + \sqrt 6)^2}{( 5-6)^2}$

$=(\sqrt 5 + \sqrt 6)^2$

No fractions in that one so FALSE.