What is the following product?
[tex]$\sqrt{10} \cdot \sqrt{10}$[/tex]
A. 10
B. [tex]$10 \sqrt{10}$[/tex]
C. 100
D. [tex]$2 \sqrt{10}$[/tex]
Answer (2)
The product of 10 and 10 is 10, which is option A. This is derived from the property that states a ⋅ a = a .
;
The problem asks to find the product of 10 and 10 .
Use the property a ⋅ a = a .
Apply the property to get 10 ⋅ 10 = 10 .
The final answer is 10 .
Explanation
Understanding the Problem We are asked to compute the product of two square roots: 10 ⋅ 10 .
Applying the Property of Square Roots We can use the property that a ⋅ a = a for any non-negative number a . In our case, a = 10 , which is non-negative, so we can apply this property.
Calculating the Product Applying the property, we have 10 ⋅ 10 = 10 .
Final Answer Therefore, the product of 10 and 10 is 10.
Examples
Square roots are used in many real-world applications, such as calculating distances and areas. For example, if you have a square garden with an area of 10 square meters, the length of each side is 10 meters. Multiplying 10 ⋅ 10 gives you the area of the garden, which is 10 square meters. This concept is also used in physics to calculate speeds and energies.
