Square and Cube Roots Quiz Set 016

We can see that 0.08 × 0.08 × 0.08 = 0.000512, so cube root is 0.08.

We know that 0.07 = $√0.0049$, so by inspection we can see that 0.0449 - 0.04 will give us 0.0049.

The given expression can be simplified to ${{(√5)^2} - {2 × 2} + {2 × √5 × √{5 × 5^2}}}/{2 × √5}$, which is same as ${5 - 4 + 50}/{2 × √5}$, which is same as ${51/{2 × √5}$. Rationalizing, we get ${51/{2 × √5} × {√5/√5}$ which gives ${51√5}/10$ which = 11.404.

By inspection, we can easily see that the formula (a - b) × (a + b) can be used to simplify like this: $√{(13)^2 - (3√5)^2}$, which is same as $√{169 - (3^2 × 5)}$, which is same as $√{169 - 45}$ = $√124$.

By inspection, $8x + √{16x^2 - 8x + 1}$ is same as $8x + √{({1 - 4x})^2}$, which is same as 8x + (1 - 4x) = 1 + 4x = 1.82.