Operations on Real Numbers Questions in English

(1 1/12) First,convert the mixed fraction into an improper fraction:
$1 \frac{25}{144} = \frac{1 \times 144 + 25}{144} = \frac{144 + 25}{144} = \frac{169}{144}$
Now,take the square root of the improper fraction:
$\sqrt{\frac{169}{144}} = \frac{\sqrt{169}}{\sqrt{144}} = \frac{13}{12}$
Finally,convert the improper fraction back into a mixed fraction:
$\frac{13}{12} = 1 \frac{1}{12}$

(A) To solve the expression $\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6}$,we use the property of radicals $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$.
First,multiply the terms inside the square roots: $\sqrt{2} \cdot \sqrt{3} = \sqrt{2 \cdot 3} = \sqrt{6}$.
Now,substitute this back into the original expression: $\sqrt{6} \cdot \sqrt{6}$.
Using the property $\sqrt{a} \cdot \sqrt{a} = a$,we get $\sqrt{6} \cdot \sqrt{6} = 6$.
Therefore,the correct answer is $6$.