Radicals Whose Radicands are Perfect Squares
A radical and its parts are explained and the procedure for simplifying a radical whose radicand is a perfect square is illustrated. A practical
Subject: radicand
Transcript: A RADICAL IS MADE UP OF A RADICAL SIGN AND A RADICAND. THIS IS THE RADICAL SIGN. THE EXPRESSION UNDER IT IS THE RADICAND. FOR NOW, WE'LL SIMPLIFY
Simplifying the Square Root of Larger Numbers
Simplifying the square root of a larger number.
Subject: radicand
Roots Other Than Square Roots
Simplifying radicals with cube roots and other roots.
Subject: radicand
Transcript: . WHENEVER THE INDEX OF A RADICAL IS AN EVEN NUMBER, THE ROOT OF THE NEGATIVE RADICAND CAN NOT BE A REAL NUMBER. BUT WHEN THE INDEX IS AN ODD NUMBER, A
Roots of Variables
Simplifying radicals with cube and other roots and variables.
Subject: radicand
Transcript: M RAISED TO THE 3/4 POWER. THIS FRACTION IS CALLED A RATIONAL EXPONENT. IT'S THE RATIO OF THE RADICAND'S EXPONENT OVER THE INDEX NUMBER. WE CAN WRITE
Simplifying a Radical by Factoring the Radicand
Simplifying a radical by factoring the radicand is demonstrated. The goal of simplifying a radical is to make an expression easier to deal with by
Subject: radicand
Transcript: A RADICAL IS FULLY SIMPLIFIED WHEN IT HAS NO PERFECT SQUARE FACTORS OTHER THAN 1 IN THE RADICAND. KEEP THAT IN MIND WHEN WE SIMPLIFY THIS RADICAL
Simplifying Radicals Using Multiplication
Radicals are simplified using multiplication, illustrating when to multiply first and then find the square root of the product and when to find the square root first and then multiply.
Subject: radicand
Transcript: MULTIPLIED THE RADICANDS FIRST, WE'D GET THE SQUARE ROOT OF 36. THAT'S ALSO EQUAL TO 6. SO WHEN WE MULTIPLY TWO NUMBERS LIKE THIS, WE HAVE A CHOICE. WE CAN
Simplifying Radicals With Variables
Using the rules for simplifying radicals with numbers in the radicand to simplify radicals with variables.
Subject: radicand
Transcript: SO FAR WE'VE ONLY SIMPLIFIED RADICALS WITH NUMBERS IN THE RADICAND. BUT WE CAN USE THE SAME RULES WE'VE LEARNED TO SIMPLIFY RADICALS WITH VARIABLES
Rationalizing the Denominator with Variables in the Radicand
Rationalizing the denominator with a variable in the radical is demonstrated.
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
Rewriting Radical Notation Using Rational Exponent Form
Finding the value of a radical by writing it in rational exponent form.
Subject: radicand
Guidelines for Simplifying Radicals
The guidelines for simplifying radicals include simplifying any perfect square in the radicand and assuring that each term in a radical expression
Subject: radicand
Transcript: RADICAND. IF A RADICAND HAD A PERFECT SQUARE FACTOR, WE SIMPLIFIED THE RADICAL. 48, FOR EXAMPLE, HAS A PERFECT SQUARE FACTOR. IT'S 16. THE OTHER FACTOR IS 3