Shortcut for Simplifying Radicals Before and After Multiplying
To avoid having to find perfect square factors for a large number by multiplying two radicals, first look for a common factor in the radicands that
Subject: radicand
Transcript: AND 15 IS 3. SO WHENEVER THERE'S A COMMON FACTOR IN THE RADICAND, WE CAN USE THIS SHORTCUT TO SIMPLIFY THE EXPRESSION. TRY IT WITH THIS PROBLEM. WE DON
Denominator of a Simplified Expression Never Has Radicals, The
A guideline is presented: a simplified radical expression never has radicals in the denominator. An expression with a radical in the denominator, but not in the numerator, is simplified using the identity property of multiplication and the process o...
Subject: radicand
Transcript: SO FAR WE'VE LEARNED SEVERAL GUIDELINES FOR SIMPLIFYING RADICALS. THERE ARE NO PERFECT SQUARE FACTORS IN THE RADICAND OF EACH TERM. EACH TERM HAS NO
Changing Rational Exponent Form to Radical Notation
Writing an expression in radical notation is detailed using several examples
Subject: radicand
Transcript: SIGN IS GREATER THAN THE INDEX, SO WE CAN SIMPLIFY FURTHER. THE RADICAND CONTAINS A PERFECT CUBE FACTOR. IT'S Y CUBED. THE OTHER FACTOR IS Y SQUARED. THE
Examples of Rationalizing the Denominator
Problems involving rationalizing the denominator are presented and a shortcut is given.
Subject: radicand
Transcript: RADICAL. WE'LL STILL MULTIPLY BY A RADICAL THAT WILL GIVE US AN INTEGER IN THE DENOMINATOR. THE PRODUCT WILL HAVE A PERFECT SQUARE IN THE RADICAND. IT WILL
Multiplying then Simplifying Two Radicals
The procedure for simplifying radicals by beginning with multiplication is demonstrated.
Subject: radicand
Transcript: SQUARE ROOT OF 35. THE SQUARE ROOT OF 35 HAS ONE RADICAL WITH NO PERFECT SQUARE FACTORS IN THE RADICAND, SO IT'S FULLY SIMPLIFIED. HERE'S ANOTHER
Dividing a Radical by a Whole Number
A radical can only be divided by another radical. In the examples demonstrated, the only radical is in the numerator. The radical simplified and the fraction reduced.
Subject: radicand
Square Root of a Negative Number is Not a Real Number, The
The square root of any negative number is not a real number. Writing a negative number in radical form is illustrated.
Subject: radicand