Use the power rule?

Question

Hi.
I have the following and want to use the power rule to solve it. How do I do it?
sqrt 98 minus sqrt 128 divided by sqrt 8 minus sqrt 2.
Thank you

Answer 1

All 4 roots can be simplified. Here's the 1st one:

sqrt (98) = sqrt (2 x 49) = sqrt (2) x sqrt (49) = sqrt (2) x 7

Also, sqrt (128) = sqrt (2 x 64) = 8 sqrt (2)

So the numerator is

7 x sqrt(2) - 8 x sqrt(2) = -1 x sqrt (2)

Similary, the bottom becomes:

2 sqrt (2) - sqrt (2) = sqrt(2)

Then, the sqrt(2) in to top cancels the sqrt(2) in the bottom.

You're left with -1, the answer.

Answer 2

the simplest root I see is sqrt(2) so find a way to factor every other term so the it looks like your other eqn
98=2*49=28(7^2)
that is 7sqrt(2)
do this for every term,
when all are to a factor of sqrt(2)
substitute x in for sqrt(2)
and solve.
if there are any x's left at the end
put sqrt(2) back in for them

Answer 3

STEP 1. - Factorize all

98= 7*7*2
128= 8*8*2
8= 2*2*2
STEP-2 (NUMERATOR)

Then SQ RT(98) -SQ RT(128) = SQ RT(7^2* 2) - SQRT(8^2 *2) = 7SQRT2- 8SQRT 2= (-1)* SQRT(2)
STEP3- DENOMINATOR

Similarly denominator = 2 SQRT(2) -SQRT(2) = SQRT(2)
STEP-4

Thus Numerator/Denominator = (-1)

( by Cancel ling SQ RT(2)

Answer = -1

Answer 4

sqrt(98) - sqrt(128) / sqrt(8) - sqrt(2)
sqrt(49*2) - sqrt(64*2) / sqrt(4*2) - sqrt(2)
7sqrt(2) - 8sqrt(2) / 2sqrt(2) - 1sqrt(2)
sqrt(2)(7-8) / sqrt(2)(2-1)
(7-8)/(2-1)
-1/1
-1

Answer 5

-1

Answer 6

The answer is -1.
sqrt 98-sqrt 128 simplifies to 7sqrt2-8sqrt2.
sqrt8-sqrt2 simplifies to 2sqrt2-sqrt2.
7sqrt2-8sqrt2=-sqrt2 and 2sqrt2-sqrt2=sqrt2.
so -sqrt2/sqrt2=-1