What are 3 numbers whose square roots can be written in the form a√3 for some integer value of a?
Help?
If √N=a√3
then
N=a²*3 = 3a²
Substitute 3 integer values of a to find 3 possible values of N.
To find three numbers whose square roots can be written in the form a√3, we need to look for numbers whose square roots involve the irrational number √3.
First, let's find the square root of 3 (√3) using a calculator or by other means. The square root of 3 is approximately 1.732.
Now, to find numbers whose square roots involve the expression a√3, we can multiply √3 by different integers (a) and square the result. This will give us numbers whose square roots can be written in the form a√3.
Let's try a few examples:
1. If we choose a = 1, then a√3 = 1√3 = √3. Now we square this value: (√3)² = 3. So, 3 is one such number.
2. If we choose a = 2, then a√3 = 2√3. Squaring this value gives: (2√3)² = (2 × 1.732)² ≈ 11.313. Thus, 11.313 is another number.
3. If we choose a = 3, then a√3 = 3√3. Squaring this value gives: (3√3)² = (3 × 1.732)² ≈ 19.448. Hence, 19.448 is the third number.
So, the three numbers whose square roots can be expressed in the form a√3 are approximately 3, 11.313, and 19.448.