Multiple Choice
Rationalize the denominator.
11. Roots, Radicals, and Complex Numbers
Multiplying, Dividing, and Rationalizing Radicals
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Identify the expression to simplify: \( (2\sqrt{5})(4\sqrt{7}) \). This is a product of two terms, each consisting of a coefficient and a square root.
Use the property of multiplication to separate coefficients and radicals: multiply the numbers outside the square roots and multiply the numbers inside the square roots separately. So, rewrite as \( (2 \times 4)(\sqrt{5} \times \sqrt{7}) \).
Multiply the coefficients: \( 2 \times 4 = 8 \). Then multiply the radicands (numbers inside the square roots): \( \sqrt{5} \times \sqrt{7} = \sqrt{5 \times 7} = \sqrt{35} \).
Combine the results from the previous step to get \( 8 \sqrt{35} \).
Check if the radicand (35) can be simplified further by factoring out perfect squares. Since 35 factors into 5 and 7, neither of which is a perfect square, the expression is already simplified.
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