Given: X=3√27+√48+√75 and Y=√12-2√48+√192. 1) Write X and Y in the form of a√b. 2) Compare X and Y. 3) Rationalize the denominator of: X/(Y+1) 4) Assume that the dimensions of the rectangle ABCD are U and V where U=√XY and V=X+Y. Calculate U and V, then evaluate the area of ABCD.

1) X=18√3 ; Y=2√3 2) X>Y 3) X/(Y+1)=(18√3(2√3-1))/11 4) U=√XY=6√3 ; V=20√3 Area=XY=360.

1) Y=18√3 ; X=2√3 2) X>Y 3) X/(Y+1)=(18√3(2√3-1))/11 4) U=√XY=3√3 ; V=2√3 Area=XY=12.

1) Rationalize the expression: √3/(3√2+√3) 2) Deduce that: √3/(3√2+√3)-(√6-11)/5 is an integer.

1) √3/(3√2+√3)=(√6-1)/5 2) √3/(3√2+√3)-(√6-11)/5=2

) √3/(3√2+√3)=(√6+1)/5 2) √3/(3√2+√3)-(√6-11)/5=12/5

Quiz

Zeinab Zeineddine 7 questions

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1The GCD of 360 and 48 is
1. A24
2. B18
3. C28
2(3×10³×3.6×(10²)^3)/(2.7×10⁻⁴)=
1. A4×10¹⁰
2. B4×10¹³
3. C4×10¹⁶
3If x=(a+b)² and y=(a-b)² then x-y=
1. A2ab
2. B3ab
3. C4ab
4If A=4√5-4 and B=5√5 then
1. AA=B
2. BA<B
3. CA>B
5Given the numbers:
A=8/3+5÷(1-2/5) ; B=(55×10³×2¹⁰)/(10⁴×2⁹) ; C=(4+√5)(4-√5) ; D=2√45+√81-3√20+2
then A=B=C=D
1. ATrue
2. BFalse
6Given: X=3√27+√48+√75 and Y=√12-2√48+√192.
1) Write X and Y in the form of a√b.
2) Compare X and Y.
3) Rationalize the denominator of: X/(Y+1)
4) Assume that the dimensions of the rectangle ABCD are U and V where U=√XY and V=X+Y.
Calculate U and V, then evaluate the area of ABCD.
1. A1) X=18√3 ; Y=2√3
  2) X>Y
  3) X/(Y+1)=(18√3(2√3-1))/11
  4) U=√XY=6√3 ; V=20√3
  Area=XY=360.
2. B1) Y=18√3 ; X=2√3
  2) X>Y
  3) X/(Y+1)=(18√3(2√3-1))/11
  4) U=√XY=3√3 ; V=2√3
  Area=XY=12.
7 1) Rationalize the expression: √3/(3√2+√3)
2) Deduce that: √3/(3√2+√3)-(√6-11)/5 is an integer.
1. A) √3/(3√2+√3)=(√6+1)/5
  2) √3/(3√2+√3)-(√6-11)/5=12/5
2. B1) √3/(3√2+√3)=(√6-1)/5
  2) √3/(3√2+√3)-(√6-11)/5=2