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Simplify.

3sqrt28

Simplify.\newline328 3 \sqrt{28}

Full solution

Q. Simplify.\newline328 3 \sqrt{28}
  1. Breakdown into Prime Factors: First, let's break down 2828 into its prime factors.\newline28=2×2×728 = 2 \times 2 \times 7
  2. Group Identical Factors: Now, we group the identical factors and use the exponent rule. 328=322×73\sqrt{28} = 3\sqrt{2^2 \times 7}
  3. Apply Product Property: Next, we apply the product property of radicals to separate the square root of the perfect square from the rest.\newline322×7=3×22×73\sqrt{2^2 \times 7} = 3 \times \sqrt{2^2} \times \sqrt{7}
  4. Simplify by Cancelling Squares: Since the square root and the square cancel each other out, we simplify. \newline3×22×7=3×2×73 \times \sqrt{2^2} \times \sqrt{7} = 3 \times 2 \times \sqrt{7}
  5. Multiply Numbers Outside: Finally, we multiply the numbers outside the square root. 3×2×7=673 \times 2 \times \sqrt{7} = 6\sqrt{7}

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