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Simplify.Multiply and remove all perfect squares from inside the square roots. Assume is positive.
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Q. Simplify.Multiply and remove all perfect squares from inside the square roots. Assume is positive.
- Write expression: Write down the expression to be simplified.We have the expression .
- Multiply coefficients and radicands: Multiply the coefficients (numbers outside the square roots) and the radicands (expressions inside the square roots) separately.The coefficients are and , so multiplying them gives us .The radicands are and , so multiplying them gives us .So now we have .
- Factor radicand: Factor the radicand to identify perfect squares.The number can be factored into , and is a perfect square (). The can be written as , where is a perfect square.So we can rewrite the radicand as .
- Take square root of perfect squares: Take the square root of the perfect squares.The square root of is , and the square root of is .So we can take these outside the square root, giving us .
- Multiply numbers and variables: Multiply the numbers and variables outside the square root.Multiplying , , and gives us .So the expression simplifies to .
