Square and Cube Roots Quiz Set 006

I will give a general solution for any n. $(√n - 1/√n)^2$ is same as $({(√n)^2 - 1}/√n)^2$ which becomes $(n - 1)^2/n$. Putting n = 8, we get ${49/8}$, which is same as: $6{1/8}$.

The given expression can be simplified to $0.0025 × x$ = $0.5^2$, which gives x = ${0.5^2}/0.0025$, which is same as $0.25/0.0025$ which gives 100.

We can see that √(4320) × √(4320) is same as √(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 ) × √(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 ) which equals √(2¹⁰ × 3⁶ × 5²), which equals (2⁵ × 3³ × 5¹), which gives 4320.

The given expression can be simplified to ${{(√11)^2} - 6 × 3}/{6 × √11}$, which is same as ${11 - 18}/{6 × √11}$, which is same as ${-7/{6 × √11}$. Rationalizing, we get ${-7/{6 × √11} × {√11/√11}$ which gives ${-7√11}/66$

The given expression is same as $√{7 + √42^2}$, which becomes $√{7 + 42}$, or $√49$ which gives 7 as the answer. Please note that squares of as many numbers should be always on your tips.