Write in simplified radical form by rationalizing the denominator.?

Question

..____ ..............____
V 10 - 6 / -5 ..V 10 + 7


Sqrt 10-6 / -5 Sqrt 10 + 7

I have this:

-6 Sqrt 4 / -35

-8+23 Sqrt 10 / 201
was the answer..
Multiply both numerator and denominator by .-5 Sqrt 10 - 7

Answer 1

Your first question with the V's is unclear.

√(10 - 6) / -5 √(10 + 7)
√(4) / -5 √(17)
√(4) / -5 √(4 * 4∙25)
√(4) / -5 √(4) √(4∙25)
1 / -5 √(4∙25)

Answer 2

The first thing to do is to simplify within the radical symbols. Thus, we have:
sqrt(4)/[-5 sqrt(17)].
The square root of 4 is +/- 2. The square root of 17 is not a rational number. The easiest way to rationalize the denominator is to remove the radical completely. This can be accomplished by multiplying the entire fraction by 1 written as sqrt(17)/sqrt(17). Doing this gives us:
[+/-2 sqrt(17)]/[(-5)(17)] = [+/-2 sqrt(17)]/(-85).

Answer 3

√10 - 6 / -5 √10 + 7 =

√4 / - 5 √10 - 7 =

2 / -5 √3 x √3 / √3 = - - ( x Means Times)

2 √3 / -5 √9 =

2 √3 / -5 x 3 =

2 √3 / - 15

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