AzizHusain

0.4545454545

x = 0.4545454545

x*100 = 45.45454545 -->

100x = 45.45454545

subtract x = 0.4545454545

99x = 45 --> x = 45/99 = 15/33.

2sqrt7 / (sqrt3 - sqrt5)

(2sqrt7) / (sqrt3 - sqrt5) * [(sqrt3 + sqrt5) / (sqrt3 + sqrt5)] -->

2(sqrt(21) + sqrt(35)) / (3 - 5) -->

2(sqrt(21) + sqrt(35)) / (-2) -->

-(sqrt(21) + sqrt(35)).

4x / (3 - sqrt6)

4x / (3 - sqrt6) * [(3 + sqrt6) / (3 + sqrt6)] -->

4x(3 + sqrt6) / (9 - 6) -->

12x + 4sqrt6 / (3) -->

4x + (4/3)sqrt6.

Yes, 3/8 is less than 3/4.

It is easiest to compare these two fractions by converting 3/4 to #/8 by multiplying both the numerator and denominator by 2 giving:

3/4 --> 6/8; therefore, 3/8 < 6/8.

(6-sqrt12)(6+sqrt12)

FOIL: 36 + 6sqrt(12) - 6sqrt(12) - 12 = 36 - 12 = 24.

(3+sqrt8)(3-sqrt8)

FOIL: 9 + 3sqrt(8) - 3sqrt(8) - 8 = 9 - 8 = 1.

Note: It may be easier to notice that both of these are a "difference of squares:"

(6-sqrt12)(6+sqrt12) is in the format (a - b)(a + b) = (a^2 - b^2) since the two middle terms [ab & -ab] cancel out.

(a^2 - b^2) --> (6^2 - (sqrt(12)^2)) --> (36 - 12) = 24.

Same for the second one --> (3^2 - (sqrt(8))^2) = (9 - 8) = 1.

I assume it should be (14√x+3√y)^2:

If so:

(14√x+3√y)(14√x+3√y)

196sqrt(x*x) + 42sqrt(xy) + 42sqrt(xy) + 9sqrt(y*y)

196x + 42sqrt(xy) + 42sqrt(xy) + 9y

196x + 84sqrt(xy) + 9y

Need more information for this equation.

8*(1/3) * 27 *(2/3) = 48.

To find the height, you need to draw a picture to visualize the situation (see picture at bottom):

Notice we have an angle of 35 degrees, an adjacent side and an opposite side.

opposite/adjacent = tan theta(angle) -->

tan(35 degrees) = opposite/28 -->

The opposite side is what we are trying to find (height of tree or simply x) -->

x = 28*tan(35 degrees) = 19.6058... --> 20 feet.

64*x^6 / (x^3) --> Cancel out the x^3 in the denominator and reduce the x^6 in the numerator to x^3 -->

64x^3 = (4x)^3

(sqrt3+sqrt5)^2 --> 

(sqrt3+sqrt5)(sqrt3+sqrt5) -->

sqrt(9) + sqrt(15) + sqrt(15) + sqrt(25) -->

3 + 2sqrt(15) + 5 -->

8 + 2sqrt(15)