Square and Cube Roots Quiz Set 003

Let the number of boxes = n. So balls in one box are also n, and therefore, balls in n boxes = $n^2$. We have been given $n^2 = 144$, which gives n = 12.

The given expression can be simplified to ${{(√2)^2} - {5 × 2} + {5 × √2 × √{2 × 2^2}}}/{5 × √2}$, which is same as ${2 - 10 + 20}/{5 × √2}$, which is same as ${12/{5 × √2}$. Rationalizing, we get ${12/{5 × √2} × {√2/√2}$ which gives ${12√2}/10$ which = 1.697.

The given expression can be simplified to ${{(√5)^2} - {2 × 3} + {2 × √5 × √{5 × 2^2}}}/{2 × √5}$, which is same as ${5 - 6 + 20}/{2 × √5}$, which is same as ${19/{2 × √5}$. Rationalizing, we get ${19/{2 × √5} × {√5/√5}$ which gives ${19√5}/10$ which = 4.249.

The given expression can be simplified to ${{(√11)^2} - 3 × 2}/{3 × √11}$, which is same as ${11 - 6}/{3 × √11}$, which is same as ${5/{3 × √11}$. Rationalizing, we get ${5/{3 × √11} × {√11/√11}$ which gives ${5√11}/33$

The given expression can be simplified to ${{(√2)^2} - {5 × 5} + {5 × √2 × √{2 × 5^2}}}/{5 × √2}$, which is same as ${2 - 25 + 50}/{5 × √2}$, which is same as ${27/{5 × √2}$. Rationalizing, we get ${27/{5 × √2} × {√2/√2}$ which gives ${27√2}/10$ which = 3.818.