Question

1 / [ ( root 3 + root 4 ) - root 7 ]

Answer 1

I'm going to go with the assumption that the intent of the person asking was how to rationalize the denominator in the following expression:

$17√+3√−2√$

If the original intent was for

17√+3–√−2–√

then Ms. Stapel has a better answer than I could make.

First, multiply by  7√+3√+2√7√+3√+2√

The result is

7√+3√+2√(7√+3√−2√)(7√+3√+2√)=7√+3√+2√(7√+3√)2−2

Expanding the portion in parentheses, you get

7√+3√+2√7+221√+3−2=7√+3√+2√8+221√

The next step is to multiply by  8−221√8−221√

The result is

(7√+3√+2√)(8−221√)(8+221√)(8−221√)=(7√+3√+2√)(8−221√)64−(4)(21)=(7√+3√+2√)(8−221√)−20

You can factor out a 2 from within the second set of parenthesis of the numerator, and cancel that 2 out with the denominator.

(7√+3√+2√)(4−21√)−10

Multiply the parenthesis.

47√−7√21√+43√−3√21√+42√−2√21√−10

Multiply products involving 2 radicals.

47√−147√+43√−63√+42√−42√−10

Simplify radicals that have perfect square factors.

47√−73√+43√−37√+42√−42√−10

Collect terms in the numerator.

7√−33√+42√−42√−10

Rearrange the numerator to put the radicals in numerical order from the largest to the smallest.

−42√+7√−33√+42√−10

Multiply by  −1−1.

42√−7√+33√−42√10

Answer 2

Answer:

0.9205564425

Step-by-step explanation: