Home > Algebra > Multiplication and Division of Radicals

How do you simplify #(6-sqrt(20))/2#?

Answer 1

Eva Abramson

#3-sqrt(5)#

Since #sqrt(20)=sqrt(4*5)=sqrt(4)*sqrt(5)=2sqrt(5)#, we can write

#(6-sqrt(20))/2=(6-2sqrt(5))/2=(cancel(2)(3-sqrt(5)))/cancel(2)=3-sqrt(5)#

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

Answer 2

Kennedy Adams

To simplify (6 - √20)/2, we can start by simplifying the square root of 20. The square root of 20 can be simplified as √(4 × 5), which further simplifies to 2√5.

Now, substituting this value back into the expression, we have (6 - 2√5)/2.

To simplify further, we can divide each term in the numerator by 2, resulting in 6/2 - 2√5/2.

This simplifies to 3 - √5.

Therefore, the simplified form of (6 - √20)/2 is 3 - √5.

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

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.