Questions: Simplify √28 to the form a√b. √28=

Transcript text: Simplify $\sqrt{28}$ to the form $a \sqrt{b}$. \[ \sqrt{28}= \]

Solution

Step 1: Factor the Number Inside the Square Root

First, we need to factor the number 28 into its prime factors. The prime factorization of 28 is:

\[ 28 = 2^2 \times 7 \]

Step 2: Simplify the Square Root

Using the property of square roots, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can simplify $\sqrt{28}$ as follows:

\[ \sqrt{28} = \sqrt{2^2 \times 7} = \sqrt{2^2} \times \sqrt{7} \]

Since $\sqrt{2^2} = 2$, we have:

\[ \sqrt{28} = 2 \times \sqrt{7} \]

The simplified form of $\sqrt{28}$ is:

\[ \boxed{2 \sqrt{7}} \]

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