Missing operators

Learning Objectives Identify the implied multiplication between a coefficient and a radical. Determine the correct arithmetic operator (+, −, ×, ÷) required to make an equation with radical expressions true. Apply the order of operations to solve problems involving radicals with a missing operator. Simplify radical expressions before determining the missing operator. Solve multi-step equations involving radical expressions where the operator is the unknown variable. Verify their solution by substituting the chosen operator back into the original equation. Distinguish between the rules for adding/subtracting like radicals and the rules for multiplying/dividing any radicals. What's hiding between 5 and √2 in the expression 5√2? 🤔 Let's become mathematical detectiv...

TermDefinitionExample Radical ExpressionAn expression that contains a root symbol (√, ∛, etc.).5√3 + √7 is a radical expression. Implied MultiplicationThe assumed multiplication operation when a number (coefficient) is placed directly next to a radical, or when two radicals are adjacent in parentheses.The expression 7√11 means 7 × √11. Like RadicalsRadicals that have the exact same index and the exact same radicand (the value inside the radical symbol).4√5 and -2√5 are like radicals. However, 4√5 and 4√3 are not. Simplified Radical FormA radical is in simplified form when the radicand has no perfect square factors (other than 1), contains no fractions, and there are no radicals in the denominator of a fraction.The simplified form of √50 is 5√2, because √50 = √(25 × 2) = 5√2. Coefficient o...

Combining Like Radicals (Addition/Subtraction) a√c ± b√c = (a ± b)√c To add or subtract radicals, they must be 'like radicals'. If they are, you add or subtract their coefficients and keep the radical part the same. Product Rule for Radicals a√b × c√d = (a × c)√(b × d) To multiply radicals, multiply the coefficients together and multiply the radicands together. The radicals do not need to be 'like'. Quotient Rule for Radicals (a√b) / (c√d) = (a/c)√(b/d) To divide radicals, divide the coefficients and divide the radicands. Place the results back into a radical expression.