Final answer:
To simplify the square root of 7 over the square root of 28, factor the denominator to simplify it to 2√7. The √7 terms cancel out, leaving the simplified result of 1/2.
Step-by-step explanation:
The question involves simplifying a fraction that includes square roots in both the numerator and the denominator. To simplify √7 over √28, you need to perform operations that will simplify the square root in the denominator and rewrite the expression in a simpler form. First, let's break down 28 into its prime factors which are 2×2×7.
Therefore, √28 can be rewritten as √(4×7), which simplifies to √4 × √7, leading to 2√7. Now, you have:
√7 ÷ 2√7
When you divide √7 by 2√7, the √7 in the numerator and denominator cancel out each other, which leaves you with 1 over 2. So the simplified form of √7 over √28 is 1/2.
To check if this answer is reasonable, one can consider that since 28 is four times 7, taking the square root of each should yield a square root of 7 in the numerator and twice that value in the denominator, which ultimately gives us 1/2 when simplified.