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- NOW PERFORM DISTRIBUTION INVOLVING RADICALS.
AND FOR A QUICK REVIEW TO MULTIPLY RADICALS,
AS LONG AS THE INDEX IS THE SAME,
WE MULTIPLY THE COEFFICIENTS, THEN WE MULTIPLY THE RADICANDS,
AND THEN SIMPLIFY THE PRODUCT IF POSSIBLE.
IN OUR FIRST EXAMPLE WE HAVE THE SQUARE ROOT
OF 7 x THE QUANTITY SQUARE ROOT OF 14 - THE SQUARE ROOT OF 2.
SO WE NEED TO DISTRIBUTE THE SQUARE ROOT 7.
SO FOR SQUARE ROOT 7 x SQUARE ROOT 14,
WE WOULD HAVE THE SQUARE ROOT OF 7 x 14 - AND THEN SQUARE ROOT
7 x 2 WOULD BE THE SQUARE ROOT OF 7 x 2.
NOW, WE DO NEED TO SIMPLIFY THE SQUARE ROOTS,
SO INSTEAD OF FINDING THIS PRODUCT, SINCE 14 = 7 x 2,
IT'LL BE HELPFUL TO SIMPLIFY THIS
IF WE WRITE THIS AS THE SQUARE ROOT OF 7 x 7 x 2.
THIS MAKES IT EASY TO IDENTIFY THE PERFECT SQUARE FACTORS.
NOTICE THAT 7 AND 2 ARE BOTH PRIME.
SO NOW WE CAN SEE THAT THIS HAS A PERFECT SQUARE FACTOR,
WHICH WOULD BE 49.
SO THIS SIMPLIFIES TO 7 SQUARE ROOT 2.
AND WE CAN SEE THIS DOES NOT HAVE ANY PERFECT SQUARE FACTORS,
SO WE HAVE MINUS SQUARE ROOT 14.
IN OUR SECOND EXAMPLE,
WE HAVE SQUARE ROOT 3 x THE QUANTITY 5 + SQUARE ROOT 3.
SO HERE WE'LL DISTRIBUTE SQUARE ROOT 3.
WE NEED TO BE A LITTLE CAREFUL HERE,
NOTICE THE 5 IS NOT UNDERNEATH THE SQUARE ROOT.
SO SQUARE ROOT 3 x 5 IS JUST GOING TO BE
5 SQUARE ROOT 3 + SQUARE ROOT 3 x SQUARE ROOT 3,
WOULD BE THE SQUARE ROOT OF 3 x 3,
WHICH IS A PERFECT SQUARE, AND THEREFORE SIMPLIFIES.
SO WE HAVE 5 SQUARE ROOT 3 + 3, WHICH IF WE WANTED TO,
WE COULD WRITE AS 3 + 5 SQUARE ROOT 3
BECAUSE OF THE COMMUNITY OF PROPERTY OF ADDITION.
OKAY, I HOPE YOU FOUND THIS HELPFUL.