Answer :
To express \(\sqrt{28}\) in its simplest radical form, let's go through the necessary steps to simplify the expression:
1. Factor the number under the square root: Start by factoring \(28\) into its prime factors.
[tex]\[ 28 = 2 \times 14 = 2 \times 2 \times 7 = 2^2 \times 7 \][/tex]
2. Rewrite the square root using the prime factors: Using the factorization, we can rewrite the square root as:
[tex]\[ \sqrt{28} = \sqrt{2^2 \times 7} \][/tex]
3. Separate the square root into two parts: Apply the property of square roots \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):
[tex]\[ \sqrt{2^2 \times 7} = \sqrt{2^2} \times \sqrt{7} \][/tex]
4. Simplify the square root of the perfect square: The square root of \(2^2\) simplifies to \(2\):
[tex]\[ \sqrt{2^2} \times \sqrt{7} = 2 \times \sqrt{7} \][/tex]
5. Combine the terms: Putting it all together, we get:
[tex]\[ \sqrt{28} = 2\sqrt{7} \][/tex]
Therefore, the simplest radical form of \(\sqrt{28}\) is:
[tex]\[ \boxed{2\sqrt{7}} \][/tex]
1. Factor the number under the square root: Start by factoring \(28\) into its prime factors.
[tex]\[ 28 = 2 \times 14 = 2 \times 2 \times 7 = 2^2 \times 7 \][/tex]
2. Rewrite the square root using the prime factors: Using the factorization, we can rewrite the square root as:
[tex]\[ \sqrt{28} = \sqrt{2^2 \times 7} \][/tex]
3. Separate the square root into two parts: Apply the property of square roots \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):
[tex]\[ \sqrt{2^2 \times 7} = \sqrt{2^2} \times \sqrt{7} \][/tex]
4. Simplify the square root of the perfect square: The square root of \(2^2\) simplifies to \(2\):
[tex]\[ \sqrt{2^2} \times \sqrt{7} = 2 \times \sqrt{7} \][/tex]
5. Combine the terms: Putting it all together, we get:
[tex]\[ \sqrt{28} = 2\sqrt{7} \][/tex]
Therefore, the simplest radical form of \(\sqrt{28}\) is:
[tex]\[ \boxed{2\sqrt{7}} \][/tex]
