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Simplify each of the following :

(i) (ii)

Simplify the following expressions :

(i) (4+) (3+)

(ii) (3+) (5 -)

(iii) ( -2)

(i) (11+) (11-)

(ii) (5+) (5-)

(iii)

(iv) (3+) (3-)

(v)

Simplify the following expressions:

(i) (ii) (iii)

Rationalise the denominator of each of the following (i-vii) :

(i) (ii) (iii) (iv) (v) (vi) (vii)

Find the value to three places of decimals of each of the following. It is given that

= 1.414, = 1.732, =2.236 and = 3.162.

(i) (ii) (iii) (iv)

(v) (vi)

Express each one of the following with rational denominator:

(iv) (v) (vi) (vii) (viii) (ix)

Rationales the denominator and simplify :

(iv) (v)

(vi)

Simplify :

(iv)

In each of the following determine rational numbers a and b.

(i) = a-b(ii)= a-

(iii) = a+b (iv) =a+b

(v) = a-b

(vi) =a+b

If x = 2+, find the value of x^{3} + .

If x = 3+, find the value of x^{2}+.

Find the value of , it being given that = 1.732 and =2.236

Find the values of each of the following correct to three places of decimals, it being given that = 1.414, = 1.732, =2.236, = 2.4495 and = 3.162.

If x =, find the value of 4x^{3}+2x^{2}-8x+7.

Write the value of (2+) (2-).

Write the reciprocal of 5 +.

Write the rationalisation factor of 7-3.

If = x+y, find the values of x and y.

If x = -1, then write the value of .

Simplify .

If a = +1, then find the value of a -.

If x = 2+, find the value of x +.

Write the rationalisation factor of -2.

If x = 3 + 2, then find the value of .

is equal to

The rationalisation factor of is

The rationalisation factor of 2+ is

If x = +2, then x - equals

If = a – b, then

The simplest rationalising of is

The simplest rationalising factor of +is

The simplest rationalising factor of 2√5 - √3 is

If x = , then (x-3)^{2} =

If x = 7+4 and xy=1, then =

If x + = 4, then x+ =

If x = , then x^{3} + =

If x = and y =, then x + y + xy =

If x = and y =, then x^{2} + xy + y^{2} =

The value of is

If =1.4142, then is equal to

If =1.414, then the value of upto three place of decimal is

The positive square of 7 + is

If x = , then x^{2} + -2 =

If , then a =

If == x+y, then