Square and Cube Roots Quiz Set 007

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

By inspection, we can easily see that the formula (a - b) × (a + b) can be used to simplify like this: $√{(17)^2 - (2√7)^2}$, which is same as $√{289 - (2^2 × 7)}$, which is same as $√{289 - 28}$ = $√261$.

We can see that 0.06 × 0.06 × 0.06 = 0.000216, so cube root is 0.06.

The given expression is same as $√{3 + √13^2}$, which becomes $√{3 + 13}$, or $√16$ which gives 4 as the answer. Please note that squares of as many numbers should be always on your tips.

Let the number of canvases = n. So dots in one canvas are also n, and therefore, dots in n canvases = $n^2$. We have been given $n^2 = 25$, which gives n = 5.