Find the difference: [tex]$\sqrt{20}-\sqrt{80}$[/tex]
Answer (1)
Simplify 20 to 2 5 .
Simplify 80 to 4 5 .
Subtract the simplified forms: 2 5 − 4 5 .
The result is − 2 5 , so the final answer is − 2 5 .
Explanation
Understanding the Problem We are asked to find the difference between 20 and 80 .
Simplifying 20 First, we simplify 20 . We can write 20 as 4 × 5 , so 20 = 4 × 5 = 4 × 5 = 2 5 .
Simplifying 80 Next, we simplify 80 . We can write 80 as 16 × 5 , so 80 = 16 × 5 = 16 × 5 = 4 5 .
Computing the Difference Now, we compute the difference: 20 − 80 = 2 5 − 4 5 .
Factoring and Simplifying We factor out 5 to get ( 2 − 4 ) 5 = − 2 5 .
Final Answer Therefore, the difference is − 2 5 .
Examples
Square roots are used in many areas of math and science. For example, when calculating the distance between two points in a coordinate plane, we use the distance formula, which involves square roots. If we have two points ( x 1 , y 1 ) and ( x 2 , y 2 ) , the distance d between them is given by d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . Simplifying square roots, as we did in this problem, can make these calculations easier.
