Simplify
sqrt80 -3 Sqrt63 - sqrt125 - sqrt175
√80 = √16√5 = 4√5
3√63 = 3*√9√7 = 3*3√7 = 9√7
√125 = √25√5 = 5√5
√175 = √25√7 = 5√7
so, you have
4√5-9√7-5√5-5√7 = -√5 - 14√7
√80 - 3√63 - √125 - √175
=√16√5 - 3√9√7 + √25√5 - √25√7
= 4√5 - 9√7 + 5√5 - 5√7
= 9√5 - 14√7
Argghh, messed up a sign
Steve is right
To simplify the given expression, let's simplify each individual square root term first:
1. Simplifying √80:
We can break down √80 into its prime factors.
80 = 2 x 2 x 2 x 2 x 5
Using perfect square property, we can write it as:
√80 = √(2^2 x 2^2 x 5) = 2 x 2 x √5 = 4√5
2. Simplifying -3√63:
Following a similar approach, let's break down √63 into its prime factors.
63 = 3 x 3 x 7
Using perfect square property, we can write it as:
√63 = √(3^2 x 7) = 3 x √7
Multiplying by -3, we have:
-3√63 = -3 x 3 x √7 = -9√7
3. Simplifying √125:
Let's break down √125 into its prime factors.
125 = 5 x 5 x 5
Using perfect square property, we can write it as:
√125 = √(5^2 x 5) = 5 x √5 = 5√5
4. Simplifying √175:
Breaking down √175 into its prime factors:
175 = 5 x 5 x 7
Using perfect square property, we can write it as:
√175 = √(5^2 x 7) = 5 √7
Now, we substitute the simplified square root terms back into the expression:
√80 - 3√63 - √125 - √175
= 4√5 - 9√7 - 5√5 - 5√7
Next, we group like terms together:
(4√5 - 5√5) - (9√7 + 5√7)
= -√5 - 14√7
Therefore, the simplified expression is -√5 - 14√7.