How do you simplify 2√12 - 7√3?

Answer 1

#-3sqrt(3)#

First of all, recall the following rule for non-negative real numbers #a# and #b#: (1) #sqrt(a*b) = sqrt(a)*sqrt(b)# For those who need a proof of this, just raise the right side to the power of #2# getting the expression under a square root on the left: #(sqrt(a)*sqrt(b))^2 = sqrt(a)*sqrt(b)*sqrt(a)*sqrt(b) =# #= sqrt(a)*sqrt(a)*sqrt(b)*sqrt(b) = a*b#, which proves the property (1) above.
Using this property (1), #2sqrt(12)-7sqrt(3) = 2sqrt(4*3) - 7sqrt(3) =# #= 2sqrt(4)*sqrt(3) - 7sqrt(3) = 4sqrt(3) - 7sqrt(3) = -3sqrt(3)#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To simplify 2√12 - 7√3, we can first simplify the square roots individually. The square root of 12 can be simplified as 2√3, and the square root of 3 remains the same.

So, the expression becomes 2√3 * 2 - 7√3.

Multiplying 2√3 by 2 gives us 4√3.

Therefore, the simplified expression is 4√3 - 7√3.

Combining like terms, we get -3√3 as the final simplified answer.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7