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What is the square root of 18 - the square root of 8?

Answer 1

Isaiah Anthony

The square root of 18 minus the square root of 8 is approximately 1.29.

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Answer 2

Abigail Allen

#sqrt2#

Since these are not like terms, they cannot be subtracted from one another. To address this, let's simplify the problem.

#sqrt18 - sqrt8#

Initially, divide each square into a prime number:

#sqrt(3*3*2) - sqrt(2*2*2)#

Now add together all the factors that we can factor out to create perfect squares:

#sqrt(3^2 *2) - sqrt(2^2 *2)#

Now factor those squares out of the radical sign. We can remove those squares from the radical because they can be squared perfectly, but we will leave the other terms behind because they can't be squared perfectly:

#3sqrt2 - 2sqrt2#

Now subtract as normal, since they are both being multiplied by #sqrt2#, they are like terms and can be subtracted:

#3sqrt2 - 2sqrt2 = color(red)(1sqrt2)#

#1sqrt2 rarr sqrt2#

Anything multiplied by #1# is itself, so #1sqrt2# is the same thing as #sqrt2#. That is the simplest form of this subtraction problem.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.