Select the correct answer.
Which expression simplifies to $2 \sqrt{15}$ ?
A. $\sqrt{17}$
B. $\sqrt{19}$
C. $\sqrt{30}$
D. $\sqrt{60}$
Answer (1)
Rewrite 2 15 as 4 ⋅ 15 .
Combine the square roots: 4 ⋅ 15 = 60 .
Compare the simplified expression with the given options.
The expression that simplifies to 2 15 is 60 .
Explanation
Understanding the Problem We are given four options: A. 17 , B. 19 , C. 30 , D. 60 . We want to find the option that simplifies to 2 15 .
Rewriting the Expression To determine which expression simplifies to 2 15 , we can rewrite 2 15 by expressing the coefficient 2 as a square root. Recall that 2 = 4 . Therefore, we can rewrite the expression as:
4 ⋅ 15
Combining Square Roots Now, we can combine the two square roots into a single square root by multiplying the numbers inside:
4 ⋅ 15 = 60
Finding the Matching Expression Comparing the simplified expression 60 with the given options, we see that option D, 60 , matches our simplified expression. Therefore, the expression that simplifies to 2 15 is 60 .
Final Answer The correct answer is D. 60 .
Examples
Understanding how to simplify and manipulate square roots is useful in many areas, such as physics and engineering, when dealing with distances, areas, and volumes. For example, if you are calculating the length of the diagonal of a rectangle with sides of length 4 and 15 , you would use the Pythagorean theorem, which involves square roots. Simplifying expressions with square roots allows for easier calculations and a better understanding of the relationships between different quantities.
