Anonymous

3rt5 -2rt2 is a square root of 53 - 12rt10 iff (3rt5 - 2rt2)^2 = 53 - 12rt10. Now (3rt5 - 2rt2)^2 = (3rt5)^2 - 2(3rt5)(2rt2) +(2rt2)^2 = 45 -2*3*2(rt5)(rt2) +8 = 53 - 12rt10. End of story.

Anonymous

To show: (3√5 - 2√2) = √(53 - 12√10) square both sides (on the right, this cancels the outside √ ) (3√5 - 2√2)^2 = 53 - 12√10 45 -12√10 + 8 = 53 - 12√10

Anonymous

(3√5 - 2√2)^2 = 9(5) - 6√10 - 6√10 + 4(2) = 45 - 12√10 + 8 = 53 - 12√10

Anonymous

Show that 3√5 - 2√2 is a square root of 53 - 12√10 ( 3√5 - 2√2)² =( 3√5)² −2×( 3√5)×(2√2)+(2√2)² =45−12√10+8 =53−12√10 Hence √(53 - 12√10) = 3√5 - 2√2

Anonymous

(3√5 - 2√2)² = (3√5)² - 2(3√5)(2√2) + (2√2)² = 45 - 2·3·2(√5√2) + 8 = 53 - 12√(5·2) = 53 - 12√10

Anonymous

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Anonymous

Why? Don't you have a calculator on your PC and can't you do it in your mind?