Square and Cube Roots Quiz Set 020

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 = 9, we get ${64/9}$, which is same as: $7{1/9}$.

The given expression can be rearranged like this: $5√3 + √{6^{2} × 3}$, which is same as $5√3 + 6√3$ which is same as $11√3 = 19.05$, from which we get $√3 = 1.73$. Next we can see that $√27 + 3√3$ is same as $√{3^{2} × 3} + 3√3$, which is same as $6√3$, which gives $6 × 1.73$ = 10.39.

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

The given expression can be simplified to ${{(√3)^2} - 6 × 3}/{6 × √3}$, which is same as ${3 - 18}/{6 × √3}$, which is same as ${-15/{6 × √3}$. Rationalizing, we get ${-15/{6 × √3} × {√3/√3}$ which gives ${-15√3}/18$

The given expression can be simplified to ${{(√5)^2} - 2 × 9}/{2 × √5}$, which is same as ${5 - 18}/{2 × √5}$, which is same as ${-13/{2 × √5}$. Rationalizing, we get ${-13/{2 × √5} × {√5/√5}$ which gives ${-13√5}/10$ which = -2.907.