Question

1 / root 9 -root 8 is equal to A. 1/2 (3 - 2 root 2 ) B. 1 / 3+ 2 root 2 C. 3 - 2 root 2 D. 3 + 2 root 2

Answer 1

Answer:A=3

B=2

#Hope it helps

Answer 2

Answer:

The correct simplified answer for the given expression is found to be: $\frac{1}{3-2\sqrt{2}}$.

Step-by-step explanation:

We are given the rational number as the following:

$\frac{1}{\sqrt{9}-\sqrt{8}}$

Now we know that if after factorising the number under the square root, if we get two of the same factors under the root, we can resolve the square root by taking one of the factors outside the root.

So, finding the factors of the terms in the denominator, we get:

9 = 3 x 3

8 = 2 x 2 x 2

This makes the given rational number something like as follows:

$=\frac{1}{\sqrt{3\times 3}-\sqrt{2\times 2 \times 2}}$

Now, simplifying the sqaure root, we get:

$=\frac{1}{3\sqrt{1}-2\sqrt{2}}$

Also, we know that the square root of 1 is always 1, so we can say:

$\frac{1}{\sqrt{9}-\sqrt{8}}=\frac{1}{3-2\sqrt{2}}$

Thus, the correct answer for the given expression is found to be:

$\frac{1}{3-2\sqrt{2}}$