Square and Cube Roots Quiz Set 013

The given expression can be simplified to ${{(√5)^2} - 2 × 4}/{2 × √5}$, which is same as ${5 - 8}/{2 × √5}$, which is same as ${-3/{2 × √5}$. Rationalizing, we get ${-3/{2 × √5} × {√5/√5}$ which gives ${-3√5}/10$ which = -0.671.

The given expression can be simplified to ${√2^4/6}$ × ${5/√2^2}$ × ${6/√5^2}$, which is same as ${2^2/6}$ × ${5/2}$ × ${6/5}$, which cancels to 2.

Let the number be n. So ${1/5} × √^3n$ = 0.3, which gives $√^3n$ = 5 × 0.3 = 1.5. so n = $1.5^3$ = 3.375.

The given expression can be simplified to ${{(√5)^2} - 3 × 2}/{3 × √5}$, which is same as ${5 - 6}/{3 × √5}$, which is same as ${-1/{3 × √5}$. Rationalizing, we get ${-1/{3 × √5} × {√5/√5}$ which gives ${-1√5}/15$

By inspection, $11x + √{16x^2 - 8x + 1}$ is same as $11x + √{({1 - 4x})^2}$, which is same as 11x + (1 - 4x) = 1 + 7x = 6.14.