Vereenvoudig (toon ALLE berekeninge) die volgende sonder om 'n sakrekenaar te gebruik: 3.1.1 $ \left( 2a^3 \right)^3$ 3.1.2 $\log_p p + \log_{1}$ 3.1.3 $\frac{\sqrt{48 - \sqrt{12}}}{2\sqrt{75}}$ - NSC Technical Mathematics - Question 3 - 2018 - Paper 1

Using the property of logarithms, we have:

$\log_p p = 1,$ since any log base of itself is equal to one.

For $\log_{1}$, the result is $0$, because anything to the power of 0 gives 1, thus: $\log_{1} = 0.$

Hence, $\log_p p + \log_{1} = 1 + 0 = 1.$

First, we simplify $\sqrt{12}$ and $\sqrt{75}$:

$\sqrt{12} = 2\sqrt{3} \\ \sqrt{75} = 5\sqrt{3}.$

Substituting these values back, we have:

$\frac{\sqrt{48 - 2\sqrt{3}}}{2 \cdot 5\sqrt{3}} = \frac{\sqrt{48 - 2\sqrt{3}}}{10\sqrt{3}}.$

Next, find $\sqrt{48 - 2\sqrt{3}}$ which is more complicated; thus we leave it as is if we cannot simplify further.