Simplifying by Adding or Subtracting Common Radical Factors
A new guideline for simplifying radicals is introduced: the terms in a fully-simplified radical expression must have no common radical factors. Simplifying a radical expression by adding or subtracting common radical factors is illustrated.
Subject: radicand
Transcript: TWO GUIDELINES. THERE ARE NO PERFECT SQUARE FACTORS IN THE RADICAND. IN THIS CASE, THAT INCLUDES EACH TERM. EACH TERM HAS NO MORE THAN ONE RADICAL. BUT
Multiplying First to Get a Perfect Square in the Radicand
Simplifying a radical by multiplying first to get a perfect square in the radicand.
Subject: radicand
Transcript: THE RADICAND. THE SQUARE ROOT OF 8Y TIMES THE SQUARE ROOT OF 2Y EQUALS THE SQUARE ROOT OF 16Y SQUARED. 5 IS THE COEFFICIENT. THE RADICAND IS A PERFECT
Simplifying to Find a Common Radical Factor
The process of simplifying to find a common radical factor is demonstrated.
Subject: radicand
Transcript: 'T SUBTRACT THE TERMS, THE RADICALS ARE NOT THE SAME. BUT LOOK AT THE RADICANDS. BOTH 18 AND 50 HAVE PERFECT SQUARE FACTORS, SO WE HAVE TO SIMPLIFY. THE PERFECT
Simplifying Radicals before Multiplying
Instances are demonstrated where simplifying radicals before multiplying are indicated.
Subject: radicand
Transcript: HAS ANY PERFECT SQUARE FACTORS. LET'S TRY 4. 96 DIVIDED BY 4 IS 24. SO TWO FACTORS OF THE RADICAND ARE 4 AND 24. THE SQUARE ROOT OF 4 IS 2. 24 HAS A
Square Root of a Product, The
Illustrations of the rule for multiplying radicals: the square root of a times the square root of b equals the square root of the product a times b.
Subject: radicand
Transcript: ROOTS OF ITS FACTORS. WE CAN USE THIS RULE TO SIMPLIFY RADICALS WHOSE RADICANDS ARE NOT PERFECT SQUARES. THE SQUARE ROOT OF 12, FOR EXAMPLE, CAN BE
Expressions That Have No Common Radical Factor
Simplifying a radical expression that has no common radical factor using subtraction.
Subject: radicand
Transcript: THE TERMS. SO THE ANSWER IS THE SQUARE ROOT OF 21 MINUS 2 TIMES THE SQUARE ROOT OF 3. THERE ARE NO PERFECT SQUARE FACTORS IN THE RADICAND. EACH TERM HAS
Square Roots of Decimal Numbers and Perfect Square Decimals
Finding the square root of a decimal is discussed, noting that any decimal that does not have an even number of places after the decimal cannot have an exact square root.
Subject: radicand
Transcript: SENSE. 5/10 TIMES 5/10 EQUALS 25/100. THE SQUARE ROOT OF 25/1,000, HOWEVER, DOES NOT HAVE A PERFECT SQUARE IN THE RADICAND. IT HAS AN ODD NUMBER OF PLACES
Two Factoring Problems
Simplifying more complex radicals with numbers and variables.
Subject: radicand
Transcript: RADICAND SEPARATELY. THE SQUARE ROOT OF 4 IS 2. X TO THE SEVENTH EQUALS X TO THE SIXTH TIMES X. Y CUBED EQUALS Y SQUARED TIMES Y. NOW LET'S SIMPLIFY THE
Two Approaches for Dividing Radicals
Two approaches to simplifying radical expressions using division when the radical in the numerator and the radical in the denominator are perfect squares. Another guideline for simplifying radicals is introduced: all fractions must be reduced to low...
Subject: radicand
Transcript: . REMEMBER THE GUIDELINES. WE HAVE A TERM WITH TWO RADICALS, SO WE'LL HAVE TO SIMPLIFY. THE RADICAND IN THE NUMERATOR IS A PERFECT SQUARE. THE SQUARE ROOT OF
Radicand Divided by Another Radicand, A
Simplifying a radical expression by dividing the radical in the numerator by the radical in the denominator.
Subject: radicand
Transcript: ROOT OF 4. THAT EQUALS 2. WE'D GET THE SAME ANSWER IF THE EXPRESSION WAS WRITTEN LIKE THIS. WE'D DIVIDE THE RADICANDS, THEN SIMPLIFY THE SQUARE ROOT OF 4