GRE Sample Test 3 Quantitative Reasoning 1

Since the fractions we’re comparing have the same numerator, the fraction with the smaller denominator will be larger.The comparison is thus:
$\sqrt{\left(1+\sqrt{\frac{1}{3}}\right)}$ vs $\sqrt{\left(1+\sqrt{\frac{1}{4}}\right)}$
To simplify the comparison, square both quantities to arrive at:
1 + $\sqrt{\frac{1}{3}}$ vs 1 + $\sqrt{\frac{1}{4}}$
Simplify further by subtracting 1 from both quantities:
$\sqrt{\frac{1}{3}}$ vs $\sqrt{\frac{1}{4}}$
Simplify further by squaring both quantities:
$\frac{1}{3}$ vs $\frac{1}{4}$
Since $\frac{1}{3}$ > $\frac{1}{4}$ , the denominator in Quantity A is greater, which means the fraction in Quantity A is smaller.