Question

Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are

Answer 1

Answer:

The values of $a$ and $b$ are $33$ and $\frac{20\sqrt{3}}{3}$, respectively.

Step-by-step explanation:

The statement is equivalent to the following mathematic expression:

$\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}$ (1)

By definition of the perfect square trinomial:

$25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}$

$33 + 20\sqrt{2} = a + b\cdot \sqrt{6}$

And by direct comparison we have the following system:

$a = 33$ (2)

$b\cdot \sqrt{6} = 20\sqrt{2}$ (3)

By (3), we solve for $b$:

$b = \frac{20}{\sqrt{3}}$

$b = \frac{20\sqrt{3}}{3}$

The values of $a$ and $b$ are $33$ and $\frac{20\sqrt{3}}{3}$, respectively.