Square and Cube Roots Quiz Set 005

The given expression can be simplified to ${{(√2)^2} - {5 × 13} + {5 × √2 × √{2 × 2^2}}}/{5 × √2}$, which is same as ${2 - 65 + 20}/{5 × √2}$, which is same as ${-43/{5 × √2}$. Rationalizing, we get ${-43/{5 × √2} × {√2/√2}$ which gives ${-43√2}/10$ which = -6.081.

We can see that 0.08 × 0.08 = 0.0064, so square root is 0.08.

We can see that √(9720) × √(30) is same as √(2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5 ) × √(2 × 3 × 5 ) which equals √(2⁴ × 3⁶ × 5²), which equals (2² × 3³ × 5¹), which gives 540.

We can see that 0.07 × 0.07 × 0.07 = 0.000343, so cube root is 0.07.

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